# Graphing Data

### Histograms

#### Frequency Distribution Tables

A frequency distribution table is a table that shows how often a data point or a group of data points appears in a given data set. To make a frequency distribution table, first divide the numbers over which the data ranges into intervals of equal length. Then count how many data points fall into each interval.

If there are many values, it is sometimes useful to go through all the data points in order and make a tally mark in the interval that each point falls. Then all the tally marks can be counted to see how many data points fall into each interval. The "tally system" ensures that no points will be missed.

Example: The following is a list of prices (in dollars) of birthday cards found in various drug stores:

 1.45 2.2 0.75 1.23 1.25 1.25 3.09 1.99 2 0.78 1.32 2.25 3.15 3.85 0.52 0.99 1.38 1.75 1.22 1.75

Make a frequency distribution table for this data.

We omit the units (dollars) while calculating. The values go from 0.52 to 3.85 , which is roughly 0.50 to 4.00 . We can divide this into 7 intervals of equal length: 0.50 - 0.99 , 1.00 - 1.49 , 1.50 - 1.99 , 2.00 - 2.49 , 2.50 - 2.99 , 3.00 - 3.49 , and 3.50 - 3.99 . Then we can count the number of data points which fall into each interval--for example, 4 points fall into the first interval: 0.75, 0.78, 0.55, and 0.99--and make a frequency distribution table:
 Intervals (in dollars) Frequency 0.50 - 0.99 4 1.00 - 1.49 7 1.50 - 1.99 3 2.00 - 2.49 3 2.50 - 2.99 3.00 - 3.49 2 3.50 - 3.99 1 Total 20

#### Making a Histogram Using a Frequency Distribution Table

A histogram is a bar graph which shows frequency distribution.
To make a histogram, follow these steps:

1. On the vertical axis, place frequencies. Label this axis "Frequency".
2. On the horizontal axis, place the lower value of each interval. Label this axis with the type of data shown (price of birthday cards, etc.)
3. Draw a bar extending from the lower value of each interval to the lower value of the next interval. The height of each bar should be equal to the frequency of its corresponding interval.

Example: Make a histogram showing the frequency distribution of the price of birthday cards.

Histogram

#### Information From a Histogram

Histograms are useful because they allow us to glean certain information at a glance. The previous example shows that more birthday cards cost between \$1.00 and \$1.49 than any other price, because the bar which corresponds to those values is highest. We can also see that twice as many cards cost between \$3.00 - \$3.49 as cost between \$3.50 - \$3.99, because the bar which corresponds to \$3.00 - \$3.49 is twice as high as the bar which corresponds to \$3.50 - \$3.99.

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