## Frequency

### Ungrouped Data

Ungrouped data is used with small amounts of data where individual values are listed. e.g. 23, 45, 67, 89

If many of these values are the same the data can be place in a frequency table. These tables can be horizontal or vertical.

e.g. Test results (out of 10) of twenty people: 3, 5, 8, 6, 3, 7, 7, 8, 5, 6, 4, 3, 6, 8, 9, 1, 4, 6, 2, 10

 Result (x) 0 1 2 3 4 5 6 7 8 9 10 Frequency (f) 0 1 1 3 2 2 4 2 3 1 1

This data, called a frequency distribution can then be shown in a bar graph. ### Grouped Discrete Data

Grouped discrete data is used when each value is likely to be different and values are placed in groups or classes.

e.g.Test results (%) of 30 people

 Score Frequency 0 − 25 3 26 − 50 8 51 − 75 12 76 − 100 7

This data is best shown in a bar graph. ### Grouped Continuous Data

A histogram is a graph that is used to show the information from a frequency distribution with grouped continuous data.

It is similar to a column graph, but the bars always touch, and the area of each column is proportional to the frequency of the score that it represents.

e.g Ages of workers in a company. Note that this is grouped data.

 Ages Frequency 15 − 25 14 26 − 35 20 36 − 45 24 46 − 55 18 56 − 65 10

Note

Because these are ages, 15 − 25 means between 15 and up to 25 A zig-zag could be placedat the beginning of the horizontal axis to show that the scale is not starting at 0.

frequency curve or polygon can also be used to show grouped data

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

e.g. For the ages of the workers. ### Finding Averages in a Frequency Distribution

The table shows the number of goals scored in 20 soccer games.

 Number of goals scored in a game Frequency(f) 0 5 1 7 2 4 3 3 4 1

Mode The mode is the most common score which is 1.

Median The median is the middle score which is between the 10th and 11th which is 1.

Mean To find the mean from a frequency table of ungrouped data each value is multiplied by its frequency.

 Number of goals scored in a game Frequency(f) f .x 0 5 0 x 5 = 0 1 7 1 x 7 = 7 2 4 2 x 4 = 8 3 3 3 x 3 = 9 4 1 4 x 1 = 4 Totals 20 28
The mean, which does not have to be a whole number is 28 ÷ 20 = 1.4

If the data was grouped, the mid-points of each group would be used to find the mean.