## Frequency Tables and Histograms

The frequency is the number of times each score, event or measurement occurs.

frequency table a table in which information or data is arranged in order.

tally can be used to help add up, in groups of five, the number of times an item occurs. Note that 1111 means 5 items.

e.g. The test results of 40 people in a test out of 10 shown below are tallied and placed in a table:

2, 7, 1, 3, 4, 5, 6, 9, 10, 3, 6, 8, 9, 6, 5, 7, 9, 2, 4, 5, 6, 7, 5, 4 , 8 , 7, 6, ,4, 5, 6, 8, 9, 3, 1, 0, 6, 8, 5, 7, 4

 Score Tally Frequency Score Tally Frequency 0 1 1 6 1111 l l 7 1 11 2 7 1111 5 2 11 2 8 l l l l 4 3 111 3 9 l l l l 4 4 1111 5 10 1 1 5 1111 1 6 Total 40

From the frequency table a bar graph can be drawn.
Bar graphs are usually used for DISCRETE data, usually whole numbers, and the result of acounting process.

### Histogram

Sometimes, when each item has a different value, data has to be grouped together.
This is often
CONTINUOUS data and is the result of items being measured.

e.g. Heights of people, lengths of leaves on a tree, times of runners.

histogram is a graph that is used to show the information from a frequency table of this type.

It is similar to a column graph but the bars are always joined together.

e.g Ages of workers in a company.

Note that this is grouped data.

 Ages Frequency 15 - 14 25 - 20 35 - 24 45 - 18 55 -65 10

15-
means greater or equal to 15 and less than 25

### Frequency Curve

This is sometimes called a frequency polygon or line graph.

A frequency curve is obtained by joining up the mid-points of the tops of the columns of the histogram.

They are useful for showing trends.

In the graph below, there would appear to be fewer workers as age increases past 40.

e.g. For the ages of the workers shown above.