cal state northridge 427 andrew ainsworth phd. statistics again? what do we want to do with...
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Cal State Northridge427Andrew Ainsworth PhD
Psy 427 - Cal State Northridge
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Statistics AGAIN?What do we want to do with statistics?Organize and Describe patterns in dataTaking incomprehensible data and converting it to:Tables that summarize the dataGraphsExtract (i.e. INFER) meaning from dataInfer POPULATION values from SAMPLESHypothesis Testing GroupsHypothesis Testing Relation/Prediction
Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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DescriptivesDisorganized DataPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
Sheet1
Comedy7Suspense8Comedy7Suspense7
Drama8Horror7Drama5Comedy6
Horror8Comedy5Drama3Drama3
Suspense7Horror8Comedy6Suspense6
Horror8Comedy6Drama7Horror9
Drama5Horror9Drama6Suspense4
Drama5Horror7Suspense3Suspense4
Horror7Suspense5Horror10Suspense5
Horror9Suspense6Comedy6Drama8
Comedy7Comedy5Comedy4Drama4
Sheet2
Sheet3
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DescriptivesReducing and Describing DataPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
Book1
Comedy7756576646ComedyDramaHorrorSuspense
Drama85553763844373
Horror887978971095374
Suspense78563764455474
6585
6585
6586
6696
7797
7897
78108
ComedyDramaHorrorSuspense
5.95.48.25.5
GenreAverage Rating
Comedy5.9
Drama5.4
Horror8.2
Suspense5.5
Sheet2
Sheet3
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DescriptivesDisplaying DataPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
Chart1
5.9
5.4
8.2
5.5
Average Rating
Genre
Average Rating
Rating of Movie Genre Enjoyment
Book1
Comedy7756576646ComedyDramaHorrorSuspense
Drama85553763844373
Horror887978971095374
Suspense78563764455474
6585
6585
6586
6696
7797
7897
78108
ComedyDramaHorrorSuspense
5.95.48.25.5
GenreAverage Rating
Comedy5.9
Drama5.4
Horror8.2
Suspense5.5
Book1
Average Rating
Genre
Average Rating
Rating of Movie Genre Enjoyment
Sheet2
Sheet3
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InferentialInferential statistics:Is a set of procedures to infer information about a population based upon characteristics from samples.Samples are taken from PopulationsSample Statistics are used to infer population parametersPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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InferentialPopulation is the complete set of people, animals, events or objects that share a common characteristicA sample is some subset or subsets, selected from the population.representative simple random sample.Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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InferentialDoes the number of hours students study per day affect the grade they are likely to receive in statistics (320)?Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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InferentialSometimes manipulation is not possible Is prediction possible?Can a relationship be established?E.g., number of cigarettes smoked by per and the likelihood of getting lung cancer,The level of child abuse in the home and the severity of later psychiatric problems.Use of the death penalty and the level of crime.Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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InferentialMeasured constructs can be assessed for co-relation (where the coefficient of correlation varies between -1 to +1)
Regression analysis can be used to assess whether a measured construct predicts the values on another measured construct (or multiple) (e.g., the level of crime given the level of death penalty usage).Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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MeasurementStatistical analyses depend upon the measurement characteristics of the data.Measurement is a process of assigning numbers to constructs following a set of rules.We normally measure variables into one of four different levels of measurement:NominalOrdinalIntervalRatioPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Ordinal MeasurementWhere Numbers Representative Relative Size OnlyPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Interval Measurement:
Where Equal Differences Between Numbers Represent Equal Differences in SizePsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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MeasurementRatio Scale MeasurementIn ratio scale measurement there are four kinds of information conveyed by the numbers assigned to represent a variable:Everything Interval Measurement Contains PlusA meaningful 0-point and therefore meaningful ratios among measurements.Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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True Zero pointPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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MeasurementRatio Scale MeasurementIf we have a true ratio scale, where 0 represents an a complete absence of the variable in question, then we form a meaningful ratio among the scale values such as:
However, if 0 is not a true absence of the variable, then the ratio 4/2 = 2 is not meaningful.Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Percentiles and Percentile RanksA percentile is the score at which a specified percentage of scores in a distribution fall belowTo say a score 53 is in the 75th percentile is to say that 75% of all scores are less than 53 The percentile rank of a score indicates the percentage of scores in the distribution that fall at or below that score. Thus, for example, to say that the percentile rank of 53 is 75, is to say that 75% of the scores on the exam are less than 53.Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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PercentileScores which divide distributions into specific proportionsPercentiles = hundredthsP1, P2, P3, P97, P98, P99Quartiles = quartersQ1, Q2, Q3Deciles = tenthsD1, D2, D3, D4, D5, D6, D7, D8, D9Percentiles are the SCORESPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Percentile RankWhat percent of the scores fall below a particular score?
Percentile Ranks are the Ranks not the scoresPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Example: Percentile RankRanking no ties just number them
Ranking with ties - assign midpoint to tiesPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
Sheet1
Score:134567810
Rank:12345678
Sheet2
Sheet3
Sheet1
Score:134567810
Rank:12345678
Score:13466888
Rank:1234.54.5777
Sheet2
Sheet3
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Steps to Calculating Percentile Ranks
Example:Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
Step 1
Step 2
Step 3
Step 4
Data
Order
Number
Assign Midpoint to Ties
Percentile Rank (Apply Formula)
9
1
1
1
2.381
5
2
2
2
7.143
2
3
3
4
16.667
3
3
4
4
16.667
3
3
5
4
16.667
4
4
6
7
30.952
8
4
7
7
30.952
9
4
8
7
30.952
1
5
9
10
45.238
7
5
10
10
45.238
4
5
11
10
45.238
8
6
12
12
54.762
3
7
13
14
64.286
7
7
14
14
64.286
6
7
15
14
64.286
5
8
16
17.5
80.952
7
8
17
17.5
80.952
4
8
18
17.5
80.952
5
8
19
17.5
80.952
8
9
20
20.5
95.238
8
9
21
20.5
95.238
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Psy 427 - Cal State Northridge*PercentileWhere XP is the score at the desired percentile, p is the desired percentile (a number between 0 and 1) and n is the number of scores)If the number is an integer, than the desired percentile is that numberIf the number is not an integer than you can either round or interpolate; for this class well just round (round up when p is below .50 and down when p is above .50)
Psy 427 - Cal State Northridge
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PercentileApply the formulaYoull get a number like 7.5 (think of it as place1.proportion)Start with the value indicated by place1 (e.g. 7.5, start with the value in the 7th place)Find place2 which is the next highest place number (e.g. the 8th place) and subtract the value in place1 from the value in place2, this distance1Multiple the proportion number by the distance1 value, this is distance2Add distance2 to the value in place1 and that is the interpolated valuePsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Example: PercentileExample 1: 25th percentile: {1, 4, 9, 16, 25, 36, 49, 64, 81}X25 = (.25)(9+1) = 2.5place1 = 2, proportion = .5Value in place1 = 4Value in place2 = 9distance1 = 9 4 = 5distance2 = 5 * .5 = 2.5Interpolated value = 4 + 2.5 = 6.56.5 is the 25th percentilePsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Example: PercentileExample 2: 75th percentile {1, 4, 9, 16, 25, 36, 49, 64, 81}X75 = (.75)(9+1) = 7.5place1 = 7, proportion = .5Value in place1 = 49Value in place2 = 64distance1 = 64 49 = 15distance2 = 15 * .5 = 7.5Interpolated value = 49 + 7.5 = 56.556.5 is the 75th percentilePsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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QuartilesTo calculate Quartiles you simply find the scores the correspond to the 25, 50 and 75 percentiles. Q1 = P25, Q2 = P50, Q3 = P75Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Reducing DistributionsRegardless of numbers of scores, distributions can be described with three pieces of info:Central TendencyVariabilityShape (Normal, Skewed, etc.)
Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Measures of Central TendencyPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
Sheet1
ScoreScore - Meandi=(Xi MX)
33 - 5.75-2.75
44 - 5.75-1.75
66 - 5.750.25
1010 - 5.754.25
0
Sheet2
MeasureDefinitionLevel of MeasurementDisadvantage
ModeMost frequent valuenom., ord., int./rat.Crude
MedianMiddle valueord., int./rat.Only two points contribute
MeanArithmetic averageint./rat.Affected by skew
Sheet3
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The MeanOnly used for interval & ratio data.
Major advantages:The sample value is a very good estimate of the population value.Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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Reducing DistributionsRegardless of numbers of scores, distributions can be described with three pieces of info:Central TendencyVariabilityShape (Normal, Skewed, etc.)
Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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How do scores spread out?VariabilityTell us how far scores spread outTells us how the degree to which scores deviate from the central tendencyPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
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How are these different?Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
Chart1
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Sheet1
-110.000145441
-10.90.000154156Mean10
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1.90.0267303605
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2.10.0279451807
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30.0336662551
3.10.0343225196
3.20.0349818583
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3.50.0369751708
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3.70.0383135041
3.80.0389844812
3.90.0396561918
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6.10.0538285877
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6.70.0571571845
6.80.0576755266
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80.0628971077
8.10.0632387271
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8.40.0641677222
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8.60.064704691
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8.80.0651736974
8.90.0653822255
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9.10.0657464733
9.20.0659018925
9.30.0660393322
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9.50.066259832
9.60.0663427092
9.70.0664072408
9.80.0664533733
9.90.0664810681
100.0664903023
10.10.0664810681
10.20.0664533733
10.30.0664072408
10.40.0663427092
10.50.066259832
10.60.0661586783
10.70.0660393322
10.80.0659018925
10.90.0657464733
110.0655732033
11.10.0653822255
11.20.0651736974
11.30.0649477908
11.40.064704691
11.50.0644445973
11.60.0641677222
11.70.0638742911
11.80.0635645425
11.90.0632387271
120.0628971077
12.10.0625399591
12.20.0621675672
12.30.061780229
12.40.0613782521
12.50.0609619544
12.60.0605316634
12.70.0600877162
12.80.0596304584
12.90.0591602445
130.0586774368
13.10.0581824052
13.20.0576755266
13.30.0571571845
13.40.0566277687
13.50.0560876744
13.60.0555373021
13.70.0549770567
13.80.0544073476
13.90.0538285877
140.0532411929
14.10.0526455821
14.20.0520421761
14.30.0514313976
14.40.0508136704
14.50.050189419
14.60.0495590681
14.70.0489230424
14.80.0482817657
14.90.0476356607
150.0469851486
15.10.0463306483
15.20.0456725765
15.30.0450113469
15.40.0443473697
15.50.0436810518
15.60.0430127955
15.70.0423429988
15.80.0416720551
15.90.041000352
160.0403282721
16.10.0396561918
16.20.0389844812
16.30.0383135041
16.40.0376436174
16.50.0369751708
16.60.0363085069
16.70.0356439603
16.80.0349818583
16.90.0343225196
170.0336662551
17.10.0330133669
17.20.0323641489
17.30.0317188858
17.40.0310778538
17.50.0304413197
17.60.0298095414
17.70.0291827675
17.80.0285612373
17.90.0279451807
180.0273348181
18.10.0267303605
18.20.0261320094
18.30.0255399567
18.40.0249543849
18.50.024375467
18.60.0238033665
18.70.0232382373
18.80.0226802241
18.90.0221294625
190.0215860784
19.10.0210501888
19.20.0205219017
19.30.0200013161
19.40.0194885221
19.50.0189836011
19.60.018486626
19.70.0179976612
19.80.0175167629
19.90.0170439791
200.0165793498
20.10.0161229074
20.20.0156746765
20.30.0152346743
20.40.0148029109
20.50.0143793891
20.60.0139641052
20.70.0135570484
20.80.0131582018
20.90.0127675422
210.0123850403
21.10.0120106609
21.20.0116443634
21.30.0112861017
21.40.0109358244
21.50.0105934753
21.60.0102589934
21.70.0099323132
21.80.0096133647
21.90.0093020742
220.0089983636
22.10.0087021515
22.20.0084133528
22.30.0081318794
22.40.0078576398
22.50.0075905398
22.60.0073304827
22.70.0070773691
22.80.0068310974
22.90.006591564
230.0063586634
23.10.0061322882
23.20.0059123296
23.30.0056986775
23.40.0054912205
23.50.0052898463
23.60.0050944415
23.70.0049048923
23.80.004721084
23.90.0045429017
240.0043702302
24.10.0042029542
24.20.0040409582
24.30.0038841269
24.40.0037323455
24.50.0035854992
24.60.0034434737
24.70.0033061555
24.80.0031734317
24.90.0030451899
250.002921319
25.10.0028017084
25.20.0026862489
25.30.0025748322
25.40.0024673512
25.50.0023637001
25.60.0022637744
25.70.0021674709
25.80.0020746878
25.90.001985325
260.0018992836
26.10.0018164665
26.20.0017367781
26.30.0016601244
26.40.0015864131
26.50.0015155537
26.60.0014474571
26.70.0013820363
26.80.0013192058
26.90.001258882
270.001200983
27.10.0011454287
27.20.0010921407
27.30.0010410427
27.40.0009920597
27.50.0009451189
27.60.0009001491
27.70.0008570809
27.80.0008158467
27.90.0007763805
280.0007386183
28.10.0007024977
28.20.0006679579
28.30.0006349399
28.40.0006033864
28.50.0005732417
28.60.0005444517
28.70.0005169641
28.80.0004907278
28.90.0004656937
290.000441814
29.10.0004190423
29.20.000397334
29.30.0003766456
29.40.0003569352
29.50.0003381623
29.60.0003202879
29.70.0003032739
29.80.000287084
29.90.0002716829
300.0002570367
30.10.0002431124
30.20.0002298786
30.30.0002173048
30.40.0002053617
30.50.0001940211
30.60.0001832558
30.70.0001730398
30.80.0001633479
30.90.000154156
310.000145441
31.10.0001371805
31.20.0001293533
31.30.0001219388
31.40.0001149174
31.50.0001082702
31.60.0001019791
31.70.0000960269
31.80.0000903971
31.90.0000850736
320.0000800414
32.10.000075286
32.20.0000707934
32.30.0000665504
32.40.0000625444
32.50.0000587631
32.60.0000551951
32.70.0000518294
32.80.0000486554
32.90.0000456631
330.0000428429
33.10.0000401857
33.20.0000376829
33.30.0000353261
33.40.0000331075
33.50.0000310197
33.60.0000290554
33.70.000027208
33.80.0000254709
33.90.0000238381
340.0000223038
34.10.0000208625
34.20.0000195088
34.30.000018238
34.40.0000170452
34.50.000015926
34.60.0000148761
34.70.0000138916
34.80.0000129686
34.90.0000121036
350.0000112932
35.10.0000105341
35.20.0000098233
35.30.0000091579
35.40.0000085352
35.50.0000079526
35.60.0000074078
35.70.0000068983
35.80.0000064221
35.90.0000059771
360.0000055615
36.10.0000051732
36.20.0000048108
36.30.0000044725
36.40.0000041568
36.50.0000038623
36.60.0000035877
36.70.0000033317
36.80.0000030931
36.90.0000028708
370.0000026638
37.10.000002471
37.20.0000022915
37.30.0000021244
37.40.000001969
37.50.0000018244
37.60.00000169
37.70.0000015651
37.80.000001449
37.90.0000013411
380.0000012409
38.10.0000011479
38.20.0000010616
38.30.0000009814
38.40.0000009071
38.50.0000008382
38.60.0000007743
38.70.000000715
38.80.0000006602
38.90.0000006093
390.0000005622
39.10.0000005187
39.20.0000004783
39.30.000000441
39.40.0000004065
39.50.0000003745
39.60.000000345
39.70.0000003177
39.80.0000002925
39.90.0000002693
400.0000002478
40.10.0000002279
40.20.0000002096
40.30.0000001927
40.40.0000001771
40.50.0000001628
40.60.0000001495
40.70.0000001373
40.80.0000001261
40.90.0000001157
410.0000001062
41.10.0000000974
41.20.0000000893
41.30.0000000819
41.40.0000000751
41.50.0000000688
41.60.000000063
41.70.0000000577
41.80.0000000529
41.90.0000000484
420.0000000443
42.10.0000000405
42.20.000000037
42.30.0000000339
42.40.000000031
42.50.0000000283
42.60.0000000258
42.70.0000000236
42.80.0000000215
42.90.0000000197
430.0000000179
43.10.0000000164
43.20.0000000149
43.30.0000000136
43.40.0000000124
43.50.0000000113
43.60.0000000103
43.70.0000000094
43.80.0000000085
43.90.0000000078
440.0000000071
44.10.0000000064
44.20.0000000059
44.30.0000000053
44.40.0000000048
44.50.0000000044
44.60.000000004
44.70.0000000036
44.80.0000000033
44.90.000000003
450.0000000027
45.10.0000000025
45.20.0000000022
45.30.000000002
45.40.0000000018
45.50.0000000017
45.60.0000000015
45.70.0000000014
45.80.0000000012
45.90.0000000011
460.000000001
46.10.0000000009
46.20.0000000008
46.30.0000000007
46.40.0000000007
46.50.0000000006
46.60.0000000006
46.70.0000000005
46.80.0000000005
46.90.0000000004
470.0000000004
47.10.0000000003
47.20.0000000003
47.30.0000000003
47.40.0000000002
47.50.0000000002
47.60.0000000002
47.70.0000000002
47.80.0000000002
47.90.0000000001
480.0000000001
48.10.0000000001
48.20.0000000001
48.30.0000000001
48.40.0000000001
48.50.0000000001
48.60.0000000001
48.70.0000000001
48.80.0000000001
48.90
490
49.10
49.20
49.30
49.40
49.50
49.60
49.70
49.80
49.90
500
50.10
50.20
50.30
50.40
50.50
50.60
50.70
50.80
50.90
510
51.10
51.20
51.30
51.40
51.50
51.60
51.70
51.80
51.90
520
52.10
52.20
52.30
52.40
52.50
52.60
52.70
52.80
52.90
530
53.10
53.20
53.30
53.40
53.50
53.60
53.70
53.80
53.90
540
54.10
54.20
54.30
54.40
54.50
54.60
54.70
54.80
54.90
550
55.10
55.20
55.30
55.40
55.50
55.60
55.70
55.80
55.90
560
56.10
56.20
56.30
56.40
56.50
56.60
56.70
56.80
56.90
570
57.10
57.20
57.30
57.40
57.50
57.60
57.70
57.80
57.90
580
58.10
58.20
58.30
58.40
58.50
58.60
58.70
58.80
58.90
590
59.10
59.20
59.30
59.40
59.50
59.60
59.70
59.80
59.90
600
60.10
60.20
60.30
60.40
60.50
60.60
60.70
60.80
60.90
610
61.10
61.20
61.30
61.40
61.50
61.60
61.70
61.80
61.90
620
62.10
62.20
62.30
62.40
62.50
62.60
62.70
62.80
62.90
630
63.10
63.20
63.30
63.40
63.50
63.60
63.70
63.80
63.90
640
64.10
64.20
64.30
64.40
64.50
64.60
64.70
64.80
64.90
650
65.10
65.20
65.30
65.40
65.50
65.60
65.70
65.80
65.90
660
66.10
66.20
66.30
66.40
66.50
66.60
66.70
66.80
66.90
670
67.10
67.20
67.30
67.40
67.50
67.60
67.70
67.80
67.90
680
68.10
68.20
68.30
68.40
68.50
68.60
68.70
68.80
68.90
690
69.10
69.20
69.30
69.40
69.50
69.60
69.70
69.80
69.90
700
70.10
70.20
70.30
70.40
70.50
70.60
70.70
70.80
70.90
710
71.10
71.20
71.30
71.40
71.50
71.60
71.70
71.80
71.90
720
72.10
72.20
72.30
72.40
72.50
72.60
72.70
72.80
72.90
730
73.10
73.20
73.30
73.40
73.50
73.60
73.70
73.80
73.90
740
74.10
74.20
74.30
74.40
74.50
74.60
74.70
74.80
74.90
750
75.10
75.20
75.30
75.40
75.50
75.60
75.70
75.80
75.90
760
76.10
76.20
76.30
76.40
76.50
76.60
76.70
76.80
76.90
770
77.10
77.20
77.30
77.40
77.50
77.60
77.70
77.80
77.90
780
78.10
78.20
78.30
78.40
78.50
78.60
78.70
78.80
78.90
790
79.10
79.20
79.30
79.40
79.50
79.60
79.70
79.80
79.90
800
80.10
80.20
80.30
80.40
80.50
80.60
80.70
80.80
80.90
810
81.10
81.20
81.30
81.40
81.50
81.60
81.70
81.80
81.90
820
82.10
82.20
82.30
82.40
82.50
82.60
82.70
82.80
82.90
830
83.10
83.20
83.30
83.40
83.50
83.60
83.70
83.80
83.90
840
84.10
84.20
84.30
84.40
84.50
84.60
84.70
84.80
84.90
850
85.10
85.20
85.30
85.40
85.50
85.60
85.70
85.80
85.90
860
86.10
86.20
86.30
86.40
86.50
86.60
86.70
86.80
86.90
870
87.10
87.20
87.30
87.40
87.50
87.60
87.70
87.80
87.90
880
88.10
88.20
88.30
88.40
88.50
88.60
88.70
88.80
88.90
890
89.10
89.20
89.30
89.40
89.50
89.60
89.70
89.80
89.90
900
90.10
90.20
90.30
90.40
90.50
90.60
90.70
90.80
90.90
910
91.10
91.20
91.30
91.40
91.50
91.60
91.70
91.80
91.90
920
92.10
92.20
92.30
92.40
92.50
92.60
92.70
92.80
92.90
930
93.10
93.20
93.30
93.40
93.50
93.60
93.70
93.80
93.90
940
94.10
94.20
94.30
94.40
94.50
94.60
94.70
94.80
94.90
950
95.10
95.20
95.30
95.40
95.50
95.60
95.70
95.80
95.90
960
96.10
96.20
96.30
96.40
96.50
96.60
96.70
96.80
96.90
970
97.10
97.20
97.30
97.40
97.50
97.60
97.70
97.80
97.90
980
98.10
98.20
98.30
98.40
98.50
98.60
98.70
98.80
98.90
990
99.10
99.20
99.30
99.40
99.50
99.60
99.70
99.80
99.90
1000
100.10
100.20
100.30
100.40
100.50
100.60
100.70
100.80
100.90
1010
101.10
101.20
101.30
101.40
101.50
101.60
101.70
101.80
101.90
1020
102.10
102.20
102.30
102.40
102.50
102.60
102.70
102.80
102.90
1030
103.10
103.20
103.30
103.40
103.50
103.60
103.70
103.80
103.90
1040
104.10
104.20
104.30
104.40
104.50
104.60
104.70
104.80
104.90
1050
105.10
105.20
105.30
105.40
105.50
105.60
105.70
105.80
105.90
1060
106.10
106.20
106.30
106.40
106.50
106.60
106.70
106.80
106.90
1070
107.10
107.20
107.30
107.40
107.50
107.60
107.70
107.80
107.90
1080
108.10
108.20
108.30
108.40
108.50
108.60
108.70
108.80
108.90
1090
109.10
109.20
109.30
109.40
109.50
109.60
109.70
109.80
109.90
1100
110.10
110.20
110.30
110.40
110.50
110.60
110.70
110.80
110.90
1110
111.10
111.20
111.30
111.40
111.50
111.60
111.70
111.80
111.90
1120
112.10
112.20
112.30
112.40
112.50
112.60
112.70
112.80
112.90
1130
113.10
113.20
113.30
113.40
113.50
113.60
113.70
113.80
113.90
1140
114.10
114.20
114.30
114.40
114.50
114.60
114.70
114.80
114.90
1150
115.10
115.20
115.30
115.40
115.50
115.60
115.70
115.80
115.90
1160
116.10
116.20
116.30
116.40
116.50
116.60
116.70
116.80
116.90
1170
117.10
117.20
117.30
117.40
117.50
117.60
117.70
117.80
117.90
1180
118.10
118.20
118.30
118.40
118.50
118.60
118.70
118.80
118.90
1190
119.10
119.20
119.30
119.40
119.50
119.60
119.70
119.80
119.90
1200
120.10
120.20
120.30
120.40
120.50
120.60
120.70
120.80
120.90
1210
121.10
121.20
121.30
121.40
121.50
121.60
121.70
121.80
121.90
1220
122.10
122.20
122.30
122.40
122.50
122.60
122.70
122.80
122.90
1230
123.10
123.20
123.30
123.40
123.50
123.60
123.70
123.80
123.90
1240
124.10
124.20
124.30
124.40
124.50
124.60
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8.80.1227565043
8.90.1243351344
90.1257942154
9.10.1271290849
9.20.1283354443
9.30.1294093821
9.40.1303473948
9.50.1311464065
9.60.131803785
9.70.1323173567
9.80.1326854183
9.90.1329067466
100.1329806047
10.10.1329067466
10.20.1326854183
10.30.1323173567
10.40.131803785
10.50.1311464065
10.60.1303473948
10.70.1294093821
10.80.1283354443
10.90.1271290849
110.1257942154
11.10.1243351344
11.20.1227565043
11.30.1210633269
11.40.1192609168
11.50.1173548736
11.60.1153510532
11.70.1132555375
11.80.1110746041
11.90.1088146952
120.1064823858
12.10.1040843523
12.20.1016273408
12.30.0991181363
12.40.0965635315
12.50.0939702971
12.60.091345153
12.70.0886947395
12.80.0860255909
12.90.0833441101
130.0806565443
13.10.0779689624
13.20.0752872348
13.30.0726170137
13.40.0699637165
13.50.0673325101
13.60.0647282978
13.70.0621557075
13.80.0596190827
13.90.0571224746
140.0546696361
14.10.0522640187
14.20.0499087699
14.30.0476067329
14.40.0453604483
14.50.0431721567
14.60.0410438035
14.70.0389770442
14.80.036973252
14.90.0350335258
150.0331586996
15.10.031349353
15.20.0296058218
15.30.0279282103
15.40.0263164037
15.50.0247700806
15.60.0232887269
15.70.0218716488
15.80.0205179868
15.90.0192267295
160.0179967272
16.10.0168267057
16.20.0157152795
16.30.0146609654
16.40.0136621949
16.50.0127173268
16.60.0118246592
16.70.010982441
16.80.010188883
16.90.0094421679
170.0087404604
17.10.0080819163
17.20.007464691
17.30.0068869474
17.40.0063468633
17.50.0058426379
17.60.0053724978
17.70.0049347025
17.80.0045275488
17.90.0041493757
180.0037985673
18.10.0034735562
18.20.0031728263
18.30.0028949142
18.40.0026384116
18.50.002401966
18.60.0021842815
18.70.0019841194
18.80.0018002982
18.90.0016316933
190.0014772366
19.10.0013359157
19.20.0012067727
19.30.0010889034
19.40.0009814557
19.50.000883628
19.60.0007946679
19.70.0007138704
19.80.0006405757
19.90.0005741681
200.0005140733
20.10.0004597572
20.20.0004107234
20.30.0003665116
20.40.0003266958
20.50.000290882
20.60.0002587066
20.70.0002298347
20.80.0002039582
20.90.0001807941
210.0001600828
21.10.0001415868
21.20.0001250887
21.30.0001103903
21.40.0000973108
21.50.0000856858
21.60.0000753658
21.70.000066215
21.80.0000581108
21.90.0000509418
220.0000446076
22.10.0000390177
22.20.0000340904
22.30.0000297522
22.40.0000259372
22.50.0000225863
22.60.0000196465
22.70.0000170704
22.80.0000148155
22.90.0000128443
230.0000111229
23.10.0000096216
23.20.0000083136
23.30.0000071755
23.40.0000061863
23.50.0000053275
23.60.0000045829
23.70.000003938
23.80.00000338
23.90.0000028979
240.0000024818
24.10.0000021231
24.20.0000018142
24.30.0000015486
24.40.0000013203
24.50.0000011245
24.60.0000009566
24.70.0000008129
24.80.00000069
24.90.0000005851
250.0000004955
25.10.0000004192
25.20.0000003543
25.30.0000002991
25.40.0000002522
25.50.0000002124
25.60.0000001787
25.70.0000001502
25.80.0000001261
25.90.0000001057
260.0000000885
26.10.0000000741
26.20.0000000619
26.30.0000000517
26.40.0000000431
26.50.0000000359
26.60.0000000299
26.70.0000000248
26.80.0000000206
26.90.0000000171
270.0000000142
27.10.0000000117
27.20.0000000097
27.30.000000008
27.40.0000000066
27.50.0000000054
27.60.0000000045
27.70.0000000037
27.80.000000003
27.90.0000000025
280.000000002
28.10.0000000017
28.20.0000000014
28.30.0000000011
28.40.0000000009
28.50.0000000007
28.60.0000000006
28.70.0000000005
28.80.0000000004
28.90.0000000003
290.0000000003
29.10.0000000002
29.20.0000000002
29.30.0000000001
29.40.0000000001
29.50.0000000001
29.60.0000000001
29.70.0000000001
29.80
29.90
300
30.10
30.20
30.30
30.40
30.50
30.60
30.70
30.80
30.90
310
31.10
31.20
31.30
31.40
31.50
31.60
31.70
31.80
31.90
320
32.10
32.20
32.30
32.40
32.50
32.60
32.70
32.80
32.90
330
33.10
33.20
33.30
33.40
33.50
33.60
33.70
33.80
33.90
340
34.10
34.20
34.30
34.40
34.50
34.60
34.70
34.80
34.90
350
35.10
35.20
35.30
35.40
35.50
35.60
35.70
35.80
35.90
360
36.10
36.20
36.30
36.40
36.50
36.60
36.70
36.80
36.90
370
37.10
37.20
37.30
37.40
37.50
37.60
37.70
37.80
37.90
380
38.10
38.20
38.30
38.40
38.50
38.60
38.70
38.80
38.90
390
39.10
39.20
39.30
39.40
39.50
39.60
39.70
39.80
39.90
400
40.10
40.20
40.30
40.40
40.50
40.60
40.70
40.80
40.90
410
41.10
41.20
41.30
41.40
41.50
41.60
41.70
41.80
41.90
420
42.10
42.20
42.30
42.40
42.50
42.60
42.70
42.80
42.90
430
43.10
43.20
43.30
43.40
43.50
43.60
43.70
43.80
43.90
440
44.10
44.20
44.30
44.40
44.50
44.60
44.70
44.80
44.90
450
45.10
45.20
45.30
45.40
45.50
45.60
45.70
45.80
45.90
460
46.10
46.20
46.30
46.40
46.50
46.60
46.70
46.80
46.90
470
47.10
47.20
47.30
47.40
47.50
47.60
47.70
47.80
47.90
480
48.10
48.20
48.30
48.40
48.50
48.60
48.70
48.80
48.90
490
49.10
49.20
49.30
49.40
49.50
49.60
49.70
49.80
49.90
500
50.10
50.20
50.30
50.40
50.50
50.60
50.70
50.80
50.90
510
51.10
51.20
51.30
51.40
51.50
51.60
51.70
51.80
51.90
520
52.10
52.20
52.30
52.40
52.50
52.60
52.70
52.80
52.90
530
53.10
53.20
53.30
53.40
53.50
53.60
53.70
53.80
53.90
540
54.10
54.20
54.30
54.40
54.50
54.60
54.70
54.80
54.90
550
55.10
55.20
55.30
55.40
55.50
55.60
55.70
55.80
55.90
560
56.10
56.20
56.30
56.40
56.50
56.60
56.70
56.80
56.90
570
57.10
57.20
57.30
57.40
57.50
57.60
57.70
57.80
57.90
580
58.10
58.20
58.30
58.40
58.50
58.60
58.70
58.80
58.90
590
59.10
59.20
59.30
59.40
59.50
59.60
59.70
59.80
59.90
600
60.10
60.20
60.30
60.40
60.50
60.60
60.70
60.80
60.90
610
61.10
61.20
61.30
61.40
61.50
61.60
61.70
61.80
61.90
620
62.10
62.20
62.30
62.40
62.50
62.60
62.70
62.80
62.90
630
63.10
63.20
63.30
63.40
63.50
63.60
63.70
63.80
63.90
640
64.10
64.20
64.30
64.40
64.50
64.60
64.70
64.80
64.90
650
65.10
65.20
65.30
65.40
65.50
65.60
65.70
65.80
65.90
660
66.10
66.20
66.30
66.40
66.50
66.60
66.70
66.80
66.90
670
67.10
67.20
67.30
67.40
67.50
67.60
67.70
67.80
67.90
680
68.10
68.20
68.30
68.40
68.50
68.60
68.70
68.80
68.90
690
69.10
69.20
69.30
69.40
69.50
69.60
69.70
69.80
69.90
700
70.10
70.20
70.30
70.40
70.50
70.60
70.70
70.80
70.90
710
71.10
71.20
71.30
71.40
71.50
71.60
71.70
71.80
71.90
720
72.10
72.20
72.30
72.40
72.50
72.60
72.70
72.80
72.90
730
73.10
73.20
73.30
73.40
73.50
73.60
73.70
73.80
73.90
740
74.10
74.20
74.30
74.40
74.50
74.60
74.70
74.80
74.90
750
75.10
75.20
75.30
75.40
75.50
75.60
75.70
75.80
75.90
760
76.10
76.20
76.30
76.40
76.50
76.60
76.70
76.80
76.90
770
77.10
77.20
77.30
77.40
77.50
77.60
77.70
77.80
77.90
780
78.10
78.20
78.30
78.40
78.50
78.60
78.70
78.80
78.90
790
79.10
79.20
79.30
79.40
79.50
79.60
79.70
79.80
79.90
800
80.10
80.20
80.30
80.40
80.50
80.60
80.70
80.80
80.90
810
81.10
81.20
81.30
81.40
81.50
81.60
81.70
81.80
81.90
820
82.10
82.20
82.30
82.40
82.50
82.60
82.70
82.80
82.90
830
83.10
83.20
83.30
83.40
83.50
83.60
83.70
83.80
83.90
840
84.10
84.20
84.30
84.40
84.50
84.60
84.70
84.80
84.90
850
85.10
85.20
85.30
85.40
85.50
85.60
85.70
85.80
85.90
860
86.10
86.20
86.30
86.40
86.50
86.60
86.70
86.80
86.90
870
87.10
87.20
87.30
87.40
87.50
87.60
87.70
87.80
87.90
880
88.10
88.20
88.30
88.40
88.50
88.60
88.70
88.80
88.90
890
89.10
89.20
89.30
89.40
89.50
89.60
89.70
89.80
89.90
900
90.10
90.20
90.30
90.40
90.50
90.60
90.70
90.80
90.90
910
91.10
91.20
91.30
91.40
91.50
91.60
91.70
91.80
91.90
920
92.10
92.20
92.30
92.40
92.50
92.60
92.70
92.80
92.90
930
93.10
93.20
93.30
93.40
93.50
93.60
93.70
93.80
93.90
940
94.10
94.20
94.30
94.40
94.50
94.60
94.70
94.80
94.90
950
95.10
95.20
95.30
95.40
95.50
95.60
95.70
95.80
95.90
960
96.10
96.20
96.30
96.40
96.50
96.60
96.70
96.80
96.90
970
97.10
97.20
97.30
97.40
97.50
97.60
97.70
97.80
97.90
980
98.10
98.20
98.30
98.40
98.50
98.60
98.70
98.80
98.90
990
99.10
99.20
99.30
99.40
99.50
99.60
99.70
99.80
99.90
1000
100.10
100.20
100.30
100.40
100.50
100.60
100.70
100.80
100.90
1010
101.10
101.20
101.30
101.40
101.50
101.60
101.70
101.80
101.90
1020
102.10
102.20
102.30
102.40
102.50
102.60
102.70
102.80
102.90
1030
103.10
103.20
103.30
103.40
103.50
103.60
103.70
103.80
103.90
1040
104.10
104.20
104.30
104.40
104.50
104.60
104.70
104.80
104.90
1050
105.10
105.20
105.30
105.40
105.50
105.60
105.70
105.80
105.90
1060
106.10
106.20
106.30
106.40
106.50
106.60
106.70
106.80
106.90
1070
107.10
107.20
107.30
107.40
107.50
107.60
107.70
107.80
107.90
1080
108.10
108.20
108.30
108.40
108.50
108.60
108.70
108.80
108.90
1090
109.10
109.20
109.30
109.40
109.50
109.60
109.70
109.80
109.90
1100
110.10
110.20
110.30
110.40
110.50
110.60
110.70
110.80
110.90
1110
111.10
111.20
111.30
111.40
111.50
111.60
111.70
111.80
111.90
1120
112.10
112.20
112.30
112.40
112.50
112.60
112.70
112.80
112.90
1130
113.10
113.20
113.30
113.40
113.50
113.60
113.70
113.80
113.90
1140
114.10
114.20
114.30
114.40
114.50
114.60
114.70
114.80
114.90
1150
115.10
115.20
115.30
115.40
115.50
115.60
115.70
115.80
115.90
1160
116.10
116.20
116.30
116.40
116.50
116.60
116.70
116.80
116.90
1170
117.10
117.20
117.30
117.40
117.50
117.60
117.70
117.80
117.90
1180
118.10
118.20
118.30
118.40
118.50
118.60
118.70
118.80
118.90
1190
119.10
119.20
119.30
119.40
119.50
119.60
119.70
119.80
119.90
1200
120.10
120.20
120.30
120.40
120.50
120.60
120.70
120.80
120.90
1210
121.10
121.20
121.30
121.40
121.50
121.60
121.70
121.80
121.90
1220
122.10
122.20
122.30
122.40
122.50
122.60
122.70
122.80
122.90
1230
123.10
123.20
123.30
123.40
123.50
123.60
123.70
123.80
123.90
1240
124.10
124.20
124.30
124.40
124.50
124.60
124.70
124.80
124.90
1250
125.10
125.20
125.30
125.40
125.50
125.60
125.70
125.80
125.90
1260
126.10
126.20
126.30
126.40
126.50
126.60
126.70
126.80
126.90
1270
127.10
127.20
127.30
127.40
127.50
127.60
127.70
127.80
127.90
1280
128.10
128.20
128.30
128.40
128.50
128.60
128.70
128.80
128.90
1290
129.10
129.20
129.30
129.40
129.50
129.60
129.70
129.80
129.90
1300
130.10
130.20
130.30
130.40
130.50
130.60
130.70
130.80
130.90
1310
131.10
131.20
131.30
131.40
131.50
131.60
131.70
131.80
131.90
1320
132.10
132.20
132.30
132.40
132.50
132.60
132.70
132.80
132.90
1330
133.10
133.20
133.30
133.40
133.50
133.60
133.70
133.80
133.90
1340
134.10
134.20
134.30
134.40
134.50
134.60
134.70
134.80
134.90
1350
135.10
135.20
135.30
135.40
135.50
135.60
135.70
135.80
135.90
1360
136.10
136.20
136.30
136.40
136.50
136.60
136.70
136.80
136.90
1370
137.10
137.20
137.30
137.40
137.50
137.60
137.70
137.80
137.90
1380
138.10
138.20
138.30
138.40
138.50
138.60
138.70
138.80
138.90
1390
139.10
139.20
139.30
139.40
139.50
139.60
139.70
139.80
139.90
1400
140.10
140.20
140.30
140.40
140.50
140.60
140.70
140.80
140.90
1410
141.10
141.20
141.30
141.40
141.50
141.60
141.70
141.80
141.90
1420
142.10
142.20
142.30
142.40
142.50
142.60
142.70
142.80
142.90
1430
143.10
143.20
143.30
143.40
143.50
143.60
143.70
143.80
143.90
1440
144.10
144.20
144.30
144.40
144.50
144.60
144.70
144.80
144.90
1450
145.10
145.20
145.30
145.40
145.50
145.60
145.70
145.80
145.90
1460
146.10
146.20
146.30
146.40
146.50
146.60
146.70
146.80
146.90
1470
147.10
147.20
147.30
147.40
147.50
147.60
147.70
147.80
147.90
1480
148.10
148.20
148.30
148.40
148.50
148.60
148.70
148.80
148.90
1490
149.10
149.20
149.30
149.40
149.50
149.60
149.70
149.80
149.90
1500
150.10
150.20
150.30
150.40
150.50
150.60
150.70
150.80
150.90
1510
151.10
151.20
151.30
151.40
151.50
151.60
151.70
151.80
151.90
1520
152.10
152.20
152.30
152.40
152.50
152.60
152.70
152.80
152.90
1530
153.10
153.20
153.30
153.40
153.50
153.60
153.70
153.80
153.90
1540
154.10
154.20
154.30
154.40
154.50
154.60
154.70
154.80
154.90
1550
155.10
155.20
155.30
155.40
155.50
155.60
155.70
155.80
155.90
1560
156.10
156.20
156.30
156.40
156.50
156.60
156.70
156.80
156.90
1570
157.10
157.20
157.30
157.40
157.50
157.60
157.70
157.80
157.90
1580
158.10
158.20
158.30
158.40
158.50
158.60
158.70
158.80
158.90
1590
159.10
159.20
159.30
159.40
159.50
159.60
159.70
159.80
159.90
1600
160.10
160.20
160.30
160.40
160.50
160.60
160.70
160.80
160.90
1610
161.10
161.20
161.30
161.40
161.50
161.60
161.70
161.80
161.90
1620
162.10
162.20
162.30
162.40
162.50
162.60
162.70
162.80
162.90
1630
163.10
163.20
163.30
163.40
163.50
163.60
163.70
163.80
163.90
1640
164.10
164.20
164.30
164.40
164.50
164.60
164.70
164.80
164.90
1650
165.10
165.20
165.30
165.40
165.50
165.60
165.70
165.80
165.90
1660
166.10
166.20
166.30
166.40
166.50
166.60
166.70
166.80
166.90
1670
167.10
167.20
167.30
167.40
167.50
167.60
167.70
167.80
167.90
1680
168.10
168.20
168.30
168.40
168.50
168.60
168.70
168.80
168.90
1690
169.10
169.20
169.30
169.40
169.50
169.60
169.70
169.80
169.90
1700
170.10
170.20
170.30
170.40
170.50
170.60
170.70
170.80
170.90
1710
171.10
171.20
171.30
171.40
171.50
171.60
171.70
171.80
171.90
1720
172.10
172.20
172.30
172.40
172.50
172.60
172.70
172.80
172.90
1730
173.10
173.20
173.30
173.40
173.50
173.60
173.70
173.80
173.90
1740
174.10
174.20
174.30
174.40
174.50
174.60
174.70
174.80
174.90
1750
175.10
175.20
175.30
175.40
175.50
175.60
175.70
175.80
175.90
1760
176.10
176.20
176.30
176.40
176.50
176.60
176.70
176.80
176.90
1770
177.10
177.20
177.30
177.40
177.50
177.60
177.70
177.80
177.90
1780
178.10
178.20
178.30
178.40
178.50
178.60
178.70
178.80
178.90
1790
179.10
179.20
179.30
179.40
179.50
179.60
179.70
179.80
179.90
1800
180.10
180.20
180.30
180.40
180.50
180.60
180.70
180.80
180.90
1810
181.10
181.20
181.30
181.40
181.50
181.60
181.70
181.80
181.90
1820
182.10
182.20
182.30
182.40
182.50
182.60
182.70
182.80
182.90
1830
183.10
183.20
183.30
183.40
183.50
183.60
183.70
183.80
183.90
1840
184.10
184.20
184.30
184.40
184.50
184.60
184.70
184.80
184.90
1850
185.10
185.20
185.30
185.40
185.50
185.60
185.70
185.80
185.90
1860
186.10
186.20
186.30
186.40
186.50
186.60
186.70
186.80
186.90
1870
187.10
187.20
187.30
187.40
187.50
187.60
187.70
187.80
187.90
1880
188.10
188.20
188.30
188.40
188.50
188.60
188.70
188.80
188.90
1890
Sheet1
Sheet2
Sheet3
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Measure of VariabilityPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
Measure
Definition
Related to:
Range
Largest - Smallest
Mode
Interquartile Range
X75 - X25
Median
Semi-Interquartile Range
(X75 - X25)/2
Average Absolute Deviation
Mean
Variance
Standard Deviation
_1220299450.unknown
_1220299451.unknown
_1220298261.unknown
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The RangeThe simplest measure of variability Range (R) = Xhighest XlowestAdvantage Easy to CalculateDisadvantagesLike Median, only dependent on two scores unstable {0, 8, 9, 9, 11, 53} Range = 53 {0, 8, 9, 9, 11, 11} Range = 11Does not reflect all scoresPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
-
Variability: IQRInterquartile Range = P75 P25 or Q3 Q1This helps to get a range that is not influenced by the extreme high and low scoresWhere the range is the spread across 100% of the scores, the IQR is the spread across the middle 50%Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
-
Variability: SIQRSemi-interquartile range=(P75 P25)/2 or (Q3 Q1)/2IQR/2This is the spread of the middle 25% of the dataThe average distance of Q1 and Q3 from the medianBetter for skewed dataPsy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
-
Variability: SIQRSemi-Interquartile rangePsy 427 - Cal State Northridge*Q1 Q2 Q3Q1 Q2 Q3
Psy 427 - Cal State Northridge
-
VarianceThe average squared distance of each score from the meanAlso known as the mean squareVariance of a sample: s2Variance of a population: s2Psy 427 - Cal State Northridge*
Psy 427 - Cal State Northridge
-
VariancePsy 427 - Cal State Northridge*When calculated for a sample
When calculated for the entire population
Psy 427 - Cal State No