In these lessons, we look at how to obtain the mode and the mean from a discrete frequency table and from a grouped frequency table.
Related Pages
Median From The Frequency Table
Central Tendency
More Statistics Lessons
Example:
Find the mode of the following set of marks.
Marks | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
Frequency | 6 | 7 | 7 | 5 | 3 |
Solution:
The marks 2 and 3 have the highest frequency. So, the modes are 2 and 3.
The above example also shows that a set of observations may have more than one mode.
If the data is summarized in a frequency table, we use the following formula to find mean.
The following diagram shows how to find the mean of discrete data or grouped data from a frequency table.
Example:
The table shows the marks obtained by a group of players in a game. Find the mean of the marks.
Marks | 0 | 1 | 2 | 3 |
---|---|---|---|---|
Frequency | 11 | 10 | 19 | 10 |
Solution:
To calculate the mean, we first add the following values to the frequency table:
Marks | 0 | 1 | 2 | 3 | |
---|---|---|---|---|---|
Frequency | 11 | 10 | 19 | 10 | Total = 50 |
Marks × Frequency | 0 × 11=0 | 1 × 10=10 | 2 × 19=38 | 3 × 10=30 | Total = 78 |
Then, we calculate the mean using the formula.
To find the mean: Multiply midpoints by frequencies, add the subtotals and divide by the total of the frequencies.
To find the mode: Look for the largest frequency and the corresponding value is the modal value or modal class.
To find the median: Calculate a running total of the frequencies - the first interval that is above half the total contains the median.
Example:
The table gives information about the number of goals scored by a football team in each match last
season.
(a) Write down the modal number of goals scored.
(b) Work out the mean number of goals scored by the team last season.
Example:
The table gives some information about the weights, in kg, of 50 suitcases at the airport check-in desk.
Work out an estimate for the mean weight.
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