Chapter 3: Frequency Distributions
A frequency distribution- presents the score values and their frequency of
occurrence. When presented in a table, the score values are listed in rank
order, with the lowest score value usually at the bottom of the table.
o The major purpose of frequency distributions is to present the scores in
such a way to facilitate ease of understanding and interpretation.
When there are many scores and the score range widely listing
individual scores results in many values with a frequency of zero and a
display fro which it is difficult to visualize the shape of the distribution
and its central tendency. Under these conditions, the individual scores
are usually grouped into class intervals and presented as a frequency
distribution of grouped scores.
The larger the interval used, the greater the ambiguity.
Constructing a Frequency Distribution of Grouped Scores
1. Find the range of the scores.
2. Determine the width of each class interval (i).
3. List the limits of each class interval, placing the interval containing the lowest
score value at the bottom.
4. Tally the raw scores into the appropriate class intervals.
5. Add the tallies for each interval to obtain the interval frequency.
Relative Frequency, Cumulative Frequency, and Cumulative Percentage
Relative Frequency Distribution- indicates the proportion of the total number
of scores that occurs in each interval.
To convert a frequency distribution into a relative frequency
distribution, the frequency for each interval is divided by the total
number of scores. Thus,
Cumulative Frequency Distribution- indicates the number of scores that fall
below the upper real limit of each interval.
The cumulative frequency for each interval is found by adding the
frequency of that interval to the frequencies of all the class
intervals below it. Cumulative Percentage Distribution- indicates the percentage of scores that
fall below the upper real limit of each interval.
The cumulative percentage for each interval is found by converting
cumulative frequencies to cumulative percentages as follows:
Percentiles are measures of relative standing. They are used extensively in
education to compare the performance of an individual to that of a reference
group. A percentile or percentile point is the value on the measurement scale
below which a specified percentage of the scores in the distribution fall.
Computation of Percentile Points
Ex. Find the 50th percentile point (P ) fo50the exam scores in table 3.8 on
page 56. P is the scale value below which 50% of the scores fall (therefore if
there are 70 scores, it is the value below which 35 scores fall). To determine
P 50thin an