Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

62 CHAPTER 2 | Frequency Distributions
STEP 2
Locate the interval that contains the value that you want to calculate.
We are looking for the 50th percentile, which is located between the values of 20% and
65% in the table. The scores (upper real limits) corresponding to these two percentages are
9.5 and 14.5, respectively. The interval, measured in terms of scores and percentages, is
shown in the following table:
X c%
14.5 65%
?? 50%
9.5 20%
STEP 3
STEP 4
Locate the intermediate value as a fraction of the total interval.
Our intermediate value is 50%, which is located in the interval between 65% and 20%.
The total width of the interval is 45 points (65 – 20 = 45), and the value of 50% is located
15 points down from the top of the interval. As a fraction, the 50th percentile is located
15
45 = 1 3 down from the top of the interval.
Use the fraction to determine the corresponding location on the other scale.
Our intermediate value, 50%, is located 1 3 of the way down from the top of the interval.
Our goal is to find the score, the X value, that also is located 1 3 of the way down from the top
of the interval.
On the score (X) side of the interval, the top value is 14.5, and the bottom value is 9.5, so
the total interval width is 5 points (14.5 – 9.5 = 5). The position we are seeking is 1 3 of the
way from the top of the interval. One-third of the total interval is
1 1 32 5 5 5 3
5 1.67 points
To find this location, begin at the top of the interval, and come down 1.67 points:
14.5 – 1.67 = 12.83
This is our answer. The 50th percentile is X = 12.83.
PROBLEMS
1. Place the following set of n = 20 scores in a frequency
distribution table.
6, 2, 2, 1, 3, 2, 4, 7, 1, 2
5, 3, 1, 6, 2, 6, 3, 3, 7, 2
2. Construct a frequency distribution table for the following
set of scores. Include columns for proportion
and percentage in your table.
Scores: 2, 7, 5, 3, 2, 9, 6, 1, 1, 2
3, 3, 2, 4, 5, 2, 5, 4, 6, 5
3. Find each value requested for the distribution of
scores in the following table.
a. n
b. ΣX
c. ΣX 2 X f
5 1
4 3
3 4
2 5
1 2