Discussion Section PSYCH 227
08/31/10
Frequency distributions, central tendency, and variability
Frequency Distributions
•
Frequency distribution
: a table showing the number of individuals located in each category
or score on the scale of measurement.
o
What is it good for? Organize and summarize the data.
•
Ungrouped frequency dist.
: data are sorted into classes of single values
•
Grouped freq. dist.:
data are sorted into classes of more than one value
Ungrouped F.D. example: 7,5,8,7,4,7,6,9,8,6
X (Score)
f
f*X
p = f/n
(relative frequency)
%
c.f.
%c.f.
9
1
9
1/10
10
10
100
8
2
16
2/10
20
9
90
7
3
21
3/10
30
7
70
6
2
12
2/10
20
4
40
5
1
5
1/10
10
2
20
4
1
4
1/10
10
1
10
∑f=n
∑(fX)= ∑X
To build the distribution:
1.
Sort scores from high to low.
2.
Count the frequency of each score
3.
Multiply X by f
4.
To find p (proportion), divide f by n for each score (total should add up to 1)
5.
Multiply p by 100 to find % (total should add up to 100%)
6.
Start from the lowest score and add up f to get the cumulative frequency
7.
% C.F. = c.f./n (TOTAL) *100%
We can find n (sample size) by summing the f column.
We can find ∑X by summing up the f*x column
n = 10
∑X = 67
Rules for building a grouped F.D. (use data from example 1 in handout)
1.
We should have about 10 class intervals
2.
The width of the intervals should be a simple, “nice” number.
3.
Bottom score in each class interval is a multiple of the interval width
4.
All intervals must be the same width and cover the entire range of scores. There cannot
be gaps between the intervals.
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View Full DocumentStep 1: find the range of scores by subtracting the lowest from the highest score in the data set.
3.78 – 2.25 = 1.53
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 Fall '10
 Fairchild
 Standard Deviation, Variance, relative frequency, total, variance standard deviation

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