Frequency Tables and Histograms

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

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

A 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.

Y8_Frequency_Tables_and_Histograms_01.gif

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.

A 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

Y8_Frequency_Tables_and_Histograms_02.gif

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.

Y8_Frequency_Tables_and_Histograms_03.gif