1 distribution summaries measures of central tendency mean median mode measures of spread range...
Post on 21-Dec-2015
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1
Distribution Summaries
Measures of central tendencyMeanMedianMode
Measures of spreadRangeStandard Deviation Interquartile Range (IQR)
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Median
The median is the point in the center of the distribution such that half of the cases are larger and half are smaller
34 54 72 73 96 128 200
54 72 73 96 128 200
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But, where?
When there are an even number of observations, there is no middle observation.There are two middle observationsThe median is between the two - half way between the two
54 72 73 96 128 200 (73+96)/2 = 84.5
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What happens?
If top value is raised?
54 72 73 96 128 200
54 72 73 96 128 400
Mean? RaisedMedian? No change
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What happens?
If bottom value is lowered?
54 72 73 96 128 200
0 72 73 96 128 200 Mean? LoweredMedian? No change
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Mode
The mode of a distribution is the value that has the most observations.
1 2 4 9 10 10 15 18 19 32
1 2 4 9 10 15 18 19 32
Mode: 10
No mode
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Compare for cohabit length Mos| Freq. 0 | 246 1 | 25 2 | 18 3 | 6 4 | 12 5 | 7 6 | 8 7 | 17 8 | 14 9 | 16 10 | 19 11 | 21 12 | 14 13 | 9 14 | 11 15 | 16 16 | 7 17 | 5 18 | 8
19 | 11 20 | 5 21 | 10 22 | 8 23 | 10 24 | 9 25 | 9 26 | 5 27 | 1 28 | 4 29 | 3 30 | 2 31 | 5 32 | 4 33 | 2 34 | 5 35 | 2 36 | 3 37 | 4 39 | 2
40 | 1 41 | 2 43 | 1 44 | 2 45 | 1 46 | 5 47 | 2 48 | 2 50 | 2 51 | 2 56 | 1 57 | 1 62 | 4 63 | 1 66 | 2 67 | 1 71 | 2 73 | 2 74 | 1
76 | 1 79 | 1 81 | 2 97 | 2 103 | 2 ------------Tot | 626
Mode: 0
Median: 5
Mean: 11.75
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GraphicallyFr
acti
on
# Months Cohabited0 5 10 15 20 25 30 35 40 45 50 103
0
.461661
ModeMedian
Mean
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Central tendency
Mean: find the “average” value
Median: find the “middle” value
Mode : find the “most common” value
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Quartile
Median is the half-way point -- half of cases are above, half are below
Quartile is the quarter point
There are 3 quarter pointsFirst quartile 25% belowSecond quartile 50% belowThird quartile 75% below
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Consider cohabitation# Months |Cohabited | Freq. Percent Cum.------------+----------------------------------- 0 | 246 39.30 39.30 1 | 25 3.99 43.29 2 | 18 2.88 46.17 3 | 6 0.96 47.12 4 | 12 1.92 49.04 5 | 7 1.12 50.16 6 | 8 1.28 51.44 . . . 13 | 9 1.44 69.01 14 | 11 1.76 70.77 15 | 16 2.56 73.32 16 | 7 1.12 74.44 17 | 5 0.80 75.24 18 | 8 1.28 76.52
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Interquartile range (IQR)
Difference between the third quartile and the first quartile, Q3 - Q1
Compare with the range - the difference between the maximum and the minimum, Max - Min
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Boxplot
Graph based on median and IQR
Lower end of box: Q1
Upper end of box: Q3
Middle line: Q2 (median)
Upper whisker: 1.5*IQR above Q3
Lower whisker: 1.5*IQR below Q1
Outliers: plotted separately
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Depression Boxplot
ces-d scale items s112-s1230 71
5 10 16.5
IQR = 16.5 - 5 = 11.5
1.5*IQR = 17.25
Upper whisker = 16.5 + 17.25 = 33.75