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

60 CHAPTER 2 | Frequency Distributions
interval identified as 20–24 is only 4 points wide. To determine the correct interval
width, you can
a. Count the individual scores in the interval. For this example, the scores are 20, 21, 22,
23, and 24 for a total of 5 values. Thus, the interval width is 5 points.
b. Use the real limits to determine the real width of the interval. For example, an interval
identified as 20–24 has a lower real limit of 19.5 and an upper real limit of 24.5
(halfway to the next score). Using the real limits, the interval width is
24.5 – 19.5 = 5 points
2. Percentiles and percentile ranks are intended to identify specific locations within a
distribution of scores. When solving percentile problems, especially with interpolation,
it is helpful to sketch a frequency distribution graph. Use the graph to make a
preliminary estimate of the answer before you begin any calculations. For example,
to find the 60th percentile, you would want to draw a vertical line through the graph
so that slightly more than half (60%) of the distribution is on the left-hand side of the
line. Locating this position in your sketch will give you a rough estimate of what the
final answer should be. When doing interpolation problems, you should keep several
points in mind:
a. Remember that the cumulative percentage values correspond to the upper real limits of
each score or interval.
b. You should always identify the interval with which you are working. The easiest way
to do this is to create a table showing the endpoints on both scales (scores and cumulative
percentages). This is illustrated in Example 2.8 on page 54.
DEMONSTRATION 2.1
A GROUPED FREQUENCY DISTRIBUTION TABLE
For the following set of N = 20 scores, construct a grouped frequency distribution table using
an interval width of 5 points. The scores are:
14, 8, 27, 16, 10, 22, 9, 13, 16, 12,
10, 9, 15, 17, 6, 14, 11, 18, 14, 11
STEP 1
Set up the class intervals.
The largest score in this distribution is X = 27, and the lowest is X = 6. Therefore, a
frequency distribution table for these data would have 22 rows and would be too large. A
grouped frequency distribution table would be better. We have asked specifically for an interval
width of five points, and the resulting table has five rows.
X
25–29
20–24
15–19
10–14
5–9
Remember that the interval width is determined by the real limits of the interval. For example,
the class interval 25–29 has an upper real limit of 29.5 and a lower real limit of 24.5. The
difference between these two values is the width of the interval—namely, 5.