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Data Collection &
Descriptive Statistics
Kate Cerri
Lynn Robinson
Julie Thompson
6/13/2006
Practical Research for Learning Communities
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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:
88 76 52 34 26
Find the mean
The mean is 55.2
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:
88 76 52 47 34 26
Find the median
The median is 49.5
The Mode
• The score that occurs most frequently.
If you have a number set of the
following:
26 89 76 34 88 76 84 83 76
76 88 84 52 88 26 95 34
Find the mode
The mode is 76
Now that you have reviewed measurements
of central tendency, calculate the mean,
median, and mode using the data from your
group’s bag of M & M® chocolates. Record
them 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:
88 76 52 34 26
Find the range
The range is 62
Calculate the range using the data from
your group’s bag of M & M® candies and
record 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, then
list the mean computed for the bag.
Standard Deviation Calculation Table
Raw number in bag Deviation from the mean
(X - X)
X
Squared deviations
(X - X)2
31
17
COLORS
9
17
13
18
Mean
X =
17.5
(mean for bag)
∑ (X - X) = 0
∑ (X - X)2 =________
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
Example:
Raw number in bag Deviation from the mean
(X - X)
X
31
13.5
31 – 17.5 =
17
- 0.5
13.5
9
- 8.5
17
- 0.5
13
- 4.5
18
0.5
X =
17.5
(mean for bag)
∑ (X - X) = 0
Squared deviations
(X - X)2
∑ (X - X)2 =________
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
Example:
Raw number in bag Deviation from the mean
(X - X)
X
Squared deviations
(X - X)2
31
13.5
182.25
(13.5)2 =
17
- 0.5
0.25
182.25
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
SUM
And the Standard Deviation is...
n Calculation Table
om the mean
- X)
Squared deviations
(X - X)2
3.5
182.25
4.5
20.25
0.5
0.25
• Step 5: Divide the sum in the bottom right
0.5
0.25
box by 5 (the # of colors – 1).
8.5
72.25
• Step 0.25
6: Take the square root of the answer
0.5
in step 5, and Voilà!
X) = 0
∑ (X - X)2 = 275.5
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
35
Green
31
Mean = 17.5
25
Brown
Orange Blue 18
17
15
17
Yellow
13
Red
9
5
M&M Colors
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
Raw scores
(X - X)
z score
31
13.5
1.82
17
- 0.5
- .06
9
- 8.5
- 1.14
17
- 0.5
- .06
13
- 4.5
- .61
18
0.5
.06
Example:
13.5 ÷ 7.42 =
•Z scores are associated with the likelihood or probability that a certain raw
score will appear in a distribution.
Check it out online!!
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
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6/13/2006
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Practical Research for Learning Communities
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