Analyzing Frequency Distributions
Five important characteristics of data:
1. Distribution: the nature or shape of the distribution of the data, such as bell-shaped,
uniform, or skewed
2. Center: a representative value, such as an average, that indicates the middle
3. Variation: a measure of the amount that the values vary among themselves; scattering
4. Outliers: sample values that lie very far away from the vast majority of the other
sample values
5. Time: changing characteristics of the data over time
relative frequency – the proportion of the total number of responses that are in the
category
cumulative frequency – the sum of the frequencies for that class and all previous classes
Frequency distributions, Cumulative Frequency distributions
Example 1: A second grade teacher gave her students a word recognition test. The test
consisted of 24 words. The kids’ scores are provided below. Use these scores to construct
frequency, cumulative frequency, percentage frequency, and cumulative percentage
distribution.
Scores: {13,12,16,20,22,17,12,22,24,18,11,17,15,17,12,13,24,18,10,11,24,17,13,20,10}
Score
Frequency Cum
freq.
Percent
freq
Cum. Per.
Dist.
Example2: Students in a statistics class were given pretest at the beginning of the semester. The test
consisted of twenty scores. Below you will find the scores obtained from twenty students in this class. Use
these scores to construct frequency, cumulative frequency, percentage frequency, and cumulative
percentage distribution and answer the questions listed below.
Scores = {20,18,10,11,16,11,16,16,11,15,10,14,15,19,17,14,15,12,12,11}
Score
Frequency
Cumulative frequency
a) ……... percent of the students scored 17 or less.
b) ……...students scored either 12 or 14.
c) 40 % of the students scored ….. or less.
Percentage frequency
Cum. Per. Dist.
Categorical frequency table – lists categories or classes of scores, along with counts or
frequencies of the number of scores that fall into each category
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Lower class limits – the smallest numbers that can actually belong to the
different classes
Upper class limits – the largest numbers that can actually belong to different
classes
Class width (interval size)– difference between 2 consecutive lower class
limits or boundaries
How to find the size of the intervals:
1. Decide on the number of classes your frequency table will contain.
2. Determine the class width by dividing the range by the number of classes, and
round up, to guarantee all of the data will be in the table
3. Select as the lower limit of the first class either the lowest score or a
convenient value slightly less than the lowest score
4. Add the class width until necessary intervals are achieved
5. Make a frequency table with tally marks and record frequencies
The class will write down their age in months, and the class will create a frequency table
with 3 classes and then again with 5 classes.
Score
Frequency Cum
freq.
Percent
freq
Cum. Per.
Dist.
Score
Frequency Cum
freq.
Percent
freq
Cum. Per.
Dist.