Frequency Distributions



A frequency distribution (or frequency table) lists categories (or classes) of data values, along with counts (or frequencies) of the number of data values that fall into each category.


Frequency Distribution:  Ages of Best Actresses




Lower class limits are the smallest numbers that can actually belong to the different classes.


Upper class limits are the largest numbers that can actually belong to the different classes.


Class boundaries are the numbers used to separate classes, but without the gaps created by class limits.


Class marks or midpoints are the values in the middle of the classes.


Class width is the difference between two consecutive lower class limits or two consecutive lower class boundaries.



Procedure for Constructing a Frequency Distribution



Step 1: Decide on the number of classes your frequency table will contain. Usually, between 5 and 20 is good.


Step 2: Determine the class width by dividing the range by the number of classes. Round your result up to a convenient value.


Step 3: Locate the starting point by selecting as the lower limit of the first class either the lowest score or a convenient value slightly less than the lowest score.


Step 4: Add the class width to the starting point to get the second lower class limit. And so on…


Step 5: List the lower class limits in a vertical column, along with the upper class limits.


Step 6: Complete the table by counting up class frequencies and filling them in.



Some other guidelines to follow:


1.      Be sure the classes are mutually exclusive.

2.      Include all classes, even if the frequency is zero.

3.      Select convenient numbers for class limits.

4.      Try to keep the class widths the same for all classes.

5.      The sum of the class frequencies must equal the total number of original data values.



As an example, construct a frequency distribution for the data below.


MA202 EXAM II TEST SCORES (University of Kentucky)


68        65        23        58        55        84        70        8          26        95        93        45

60        61        69        89        59        36        92        82        57        80        77        77

70        52        49        60        77        88        72        66        64        60        44        30



A relative frequency distribution uses the same class limits as a frequency table, but relative frequencies are used instead of actual frequencies.


Relative frequency = Class frequency / Sum of all frequencies


As an example, construct relative frequency distributions for ages of Oscar-winning actresses and actors, and compare the results.



Interpreting Frequency Distributions



One important objective of organizing data into a frequency distribution is to identify the nature (or “shape”) of the distribution.



As an example, one thousand women were randomly selected and their heights were measured. The results are summarized in the following frequency distribution.



Note that the frequencies start low, increase to some maximum frequency, and then decrease to a low frequency. Note also that the distribution is approximately symmetric. Such a distribution is said to be approximately normal.



What does the frequency distribution below suggest?



Last Digits of Home-Run Distances