# Counting as Statistics

The first skill a statistician must have is to be able to count. In paticular, to count the number of objects with a specified characteristic. For example, one might have 3 people who are 72 inches tall, 2 who are 74 inches tall, 5 who are 69 inches tall, and 4 who are 65 inches tall. One might have 7 green balls, 10 red balls, and 3 yellow balls. The number of each type (i.e., 3, 2, 5, or 4 for height; 7, 10, 3 for color) is called the frequency. Such information is often communicated graphically with a bar chart or pie chart as we illustrate for the color of balls:

```              10_         __
|  |
|  |
__   |  |
number       |  |  |  |
of     5_  |  |  |  |
balls       |  |  |  |
|  |  |  |   __
|  |  |  |  |  |
|  |  |  |  |  |
___|__|__|__|__|__|___
G     R     Y

color of balls

Frequency of Ball Colors

```

Note that we may divide the number (frequency) of each type by the total number (inthis case 7+10+3=20) to get the percent or relative frequency of each type. This information can also be displayed in a bar chart or pie chart:

```              50%_        __
|  |
|  |
__   |  |
number       |  |  |  |
of    25%_ |  |  |  |
balls       |  |  |  |
|  |  |  |   __
|  |  |  |  |  |
|  |  |  |  |  |
___|__|__|__|__|__|___
G     R     Y

color of balls

Relative Frequency of Ball Colors

```

Note that the frequency or relative frequency of any sort of characteristic can be displayed with a bar or pie chart. Note also that some information which is not count information (such as miles per gallon of different cars) can be displayed as a bar chart, but cannot be displayed as a pie chart since the information is not parts of a whole.

```                          __
|  |
20_  __   |  |
MPG          |  |  |  |   __
|  |  |  |  |  |
|  |  |  |  |  |
___|__|__|__|__|__|___
GM    BMW  Ford

Make of car

```

Caveat: Although much data (i.e., frequency or relative frequency of any sort of characteristic) can be presented with either a bar chart or a pie chart, there is some information that can only be presented with a bar chart. Pie charts divide a whole, and emphasize what portion of the whole each category comprises. Raw (count) data provides a whole (all the items counted), but one often has processed data such as per capita income where adding all the numbers together does not provide a whole, or disparate data such as the IQ's of Senators, where adding the numbers together does not provide a total intelligence; the latter types of data can be presented with a bar chart, but not a pie chart. Pie charts are appropriate when one wants to emphasize what portion of the whole each category is (compare the pie and bar charts above for this purpose), but bar charts are best for identifying which categories are largest (have you ever tried to choose the largest piece of a pie? it is easier to choose the biggest (longest) brownie.

The miles per gallon information for different car manufacturers (not real data) displayed as a bar chart below could not be displayed as a pie chart since the information is not parts of a whole.

```                          __
|  |
20_  __   |  |
MPG          |  |  |  |   __
|  |  |  |  |  |
|  |  |  |  |  |
___|__|__|__|__|__|___
GM    BMW  Ford

Make of car

```
Competency: Represent the data set {CJJMCJMMJCMMM} of the religion (Christian, Muslim, Jewish) of 13 people interviewed in Jeruselem with both a bar chart and a pie chart; label them with both absolute and relative frequencies.
Identify some information that could be displayed with a bar chart, but not a pie chart.

Reflection: What are all the decisions which you must make in order to represent a data set with a bar chart or pie chart?
What are the advantages and disadvantages of a bar chart versus pie chart?

Challenge: If you had the per capita income of the New England states, how could you modify that information to represent it in a pie chart?

July 2007