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
e.g.Test results (%) of 30 people
This data is best shown in a bar graph.
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.
Note Because these are ages, 15 − 25 means between 15 and up to 25 
A zigzag could be placedat the beginning of the horizontal axis to show that the scale is not starting at 0. 
A frequency curve or polygon can also be used to show grouped data
A frequency curve is obtained by joining up the midpoints 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

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