Frequency tables - discrete data and summary statistics

frequency table and graph are summaries of the results of an activity. You can use these tables or graphs to discover or estimate the:

• mode;

• median;

• mean;

• quartiles; and

• inter-quartile range.

These are the results from 20 rolls of a die. Fill in the key summary statistics for this data once you have made the calculation

Die result	Frequency
1	1
2	5
3	4
4	4
5	3
6	3
	Total = 20

Mode = ?

Mean = ?

Lower quartile = ?

Median = ?

Upper quartile = ?

Interquartile range = ?

Possible answers

Which score occurs most often? The mode = 2.

Add up all the values and divide by 20 (the number of rolls of the die). Mean = 3.6.

Which score has 25% of the results below it? Lower quartile = 2.

Which score is the middle value? For 20 scores the middle value is between the tenth and eleventh score in order from the lowest to highest. Median = 3.5.

Which score has 75% of the results below it? Upper quartile = 5.

What is the difference between the upper and lower quartiles? Interquartile range = 3.

Mean from frequency tables - discrete data

Heather asks her friends to tell her the size of their families. She records the data in a frequency table.

Family size	Frequency	Number of people
1	0	0
2	2	4
3	5	15
4	8	32
5	4	20
6	0	0
7	1	7
	20	78

To calculate the mean number of people in each family we need to find the total number of people in the survey and the number of families.

In this survey a total of 20 families were surveyed and it was found that there were 78 people altogether.

Therefore the mean = 78/20 = 3.9 people per family.

Finding the mean from a discrete frequency table

• The frequency table tells you how many there are for each value.

• So you can work out the sub-total value of the results in each column by multiplying: value x frequency.

• Then you can add them all to find the grand total of these sub-totals.

• The mean is just the average. So you divide the grand total by the total frequency: total value divided by total frequency = mean.