6/13/2006 Practical Research for Learning Communities

Data Collection &Descriptive Statistics

Kate CerriLynn RobinsonJulie Thompson

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Steps for data collection

• Create a data collection form to organize the data collected.

• Create a coding strategy to represent data on the form.

• Collect the actual data.• Enter the data on the form.

The ten commandments of data collection

• Consider the type of data to be collected.• Determine where data will be collected.• Design a data collection form that is

clear & easy to use.• Copy the data file & keep it in a separate

location.• Be certain that any other people who

collect or transfer the data are trained & understand the data collection process.

The ten commandments of data collection

• Plan a detailed schedule of when & where the data will be collected.

• Cultivate possible sources for the participant pool.

• Follow up on participants who missed their testing session or interview.

• Never discard original data.• Follow the previous nine rules!

Measures of Central Tendency

• Mean

• Median

• Mode

The Mean

• The sum of a set of scores divided by the number of scores.If you have a number set of the following:

The mean is 55.2

Find the mean

88 76 52 34 26

The Median

• The score or the point in a distribution above which one-half of the scores lie.If you have a number set of the following:

The median is 49.5

Find the median

88 76 52 47 34 26

The Mode

• The score that occurs most frequently.If you have a number set of the following:

The mode is 76

Find the mode

26 89 76 34 88 76 84 83 76 76 88 84 52 88 26 95 34

Now that you have reviewed measurementsof central tendency, calculate the mean,median, and mode using the data from yourgroup’s bag of M & M® chocolates. Recordthem on your worksheet.

Measures of Variability

• Range

• Standard Deviation

• Variance

The Range

• The difference between the highest & lowest scores in a distribution.If you have a number set of the following:

The range is 62

Find the range

88 76 52 34 26

Calculate the range using the data fromyour group’s bag of M & M® candies andrecord it on your worksheet.

The Standard Deviation

• The average amount that each of the individual scores varies from the mean of the set scores.Your group will find the standard deviation with the data from your bag of M & M®s.

Don’t panic!!

We’ll guide you step by step!

Calculating the Standard Deviation

• Step 1: List the original color totals, thenlist the mean computed for the bag.

Standard Deviation Calculation Table Raw number in bag

X Deviation from the mean

(X - X) Squared deviations

(X - X)2

31

17

9

17

13

18

X = 17.5

(mean for bag)

∑ (X - X) = 0

∑ (X - X)2 =________

Mean

COLORS

Calculating the Standard Deviation

•Step 2: Subtract the bag’s mean from each color total and list it in the middle column.

Standard Deviation Calculation Table Raw number in bag

X Deviation from the mean

(X - X) Squared deviations

(X - X)2

31 13.5

17 - 0.5

9 - 8.5

17 - 0.5

13 - 4.5

18 0.5

X = 17.5

(mean for bag)

∑ (X - X) = 0

∑ (X - X)2 =________

Example:

31 – 17.5 =13.5

Calculating the Standard Deviation

•Steps 3 & 4: Square each deviation, & list it in the last column. Find the sum of the deviations and list it in the bottom box.

Standard Deviation Calculation Table Raw number in bag

X Deviation from the mean

(X - X) Squared deviations

(X - X)2

31 13.5 182.25

17 - 0.5 0.25

9 - 8.5 72.25

17 - 0.5 0.25

13 - 4.5 20.25

18 0.5 0.25

X = 17.5

(mean for bag)

∑ (X - X) = 0

∑ (X - X)2 = 275.5

Example:

(13.5)2 =

182.25

SUM

And the Standard Deviation is...

• Step 5: Divide the sum in the bottom right box by 5 (the # of colors – 1).

• Step 6: Take the square root of the answer in step 5, and Voilà!

In the example, divide 275.5 by 5 to get 55.1, then take the square root to get

7.42

Variance

• The square of the standard deviation.• It represents everything in the

formula for the standard deviation except the square root, and is often cited in research reports.

For the set of M& M®s, the variance is 55.1

M & M® Single Bag Distribution

Red9

Yellow13

Orange17

Blue17

Brown18

Green31

5

15

25

35

M&M Colors

Mean = 17.5

The Normal (Bell-Shaped) Curve

• The mean, median and mode are all the same value, represented by the red line.

• The two halves of the curve mirror one another.

• The tails of the curve get closer and closer to the X axis, but never touch it.

• Mean and standard deviation define characteristics of the normal curve.

Characteristics of a Normal Distribution

• The distance between the mean of the distribution and either ±1s (standard deviation) covers 34% of the area beneath the normal curve.

• Because the curve is symmetrical, 68% of the distribution falls between +1s and -1s around the mean.

• Scores are more likely to fall toward the middle than toward the extremes.

-1s

+1s

Standard Scores

• Standard scores have the same reference point and the same standard deviation.

• Are useful for accurate comparison of scores from different distributions.

• Z scores are the most frequent type of standard score.The formula:

z = (X - X) s

Z scores and their implications

Remember:s = 7.42

Example:13.5 ÷ 7.42 =

Raw scores

(X - X)

z score

31 13.5

17 - 0.5 - .06

9 - 8.5 - 1.14

17 - 0.5 - .06

13 - 4.5 - .61

18 0.5 .06

1.82

•Z scores are associated with the likeli- hood or probability that a certain raw score will appear in a distribution.

6/13/2006 Practical Research for Learning Communities

Introduction to descriptive statistics:http://www.mste.uiuc.edu/hill/dstat/dstat.html

Statistics tutorial & links elsewhere:http://www.meandeviation.com/tutorials/stats/notes/outline.html

Check it out online!!

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