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.

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.

* *

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*