 # Mode and Mean from Frequency Table

In these lessons, we will look at how to obtain the mode and the mean from a discrete frequency table and from a grouped frequency table.

Related Topics:
Median from a Frequency Table
More Statistics Lessons

### Mode from frequency table

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.

### Mean from frequency table

If the data is summarized in a frequency table, we use the following formula to find mean: 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 How to obtain the mean, median and mode from a frequency table?
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. How to find the mean for discrete data and continuous (grouped) data? How to calculate the modal average and mean average from a discrete frequency table?
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. How to calculate the estimated mean from a grouped frequency table?
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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