When data is given in a discrete frequency distribution, values are listed together with how often they occur. Measures of average and spread can still be found, but the frequencies must be taken into account.

 

 

Understanding a Discrete Frequency Distribution

A discrete frequency distribution shows:
• each possible data value
• the frequency for each value

 

Each value may occur more than once, so it must be counted according to its frequency.

Often represented in a table with Category/Value, Tally and Frequency columns.

 

 

Finding the Mean

The mean is the average value of the data.

 

To find the mean from a frequency table:

 

Multiply each data value by its frequency to find the total contribution of that value.

 

Add all these results together to find the total of all values.

 

Add all the frequencies together to find the total number of data values.

 

Divide the total of all values by the total frequency.

 

The mean takes every value and its frequency into account.

 

Large frequencies have a greater effect on the mean

 

 

Finding the Median

The median is the middle value when all data values are put in order.

 

To find the median from a frequency table:

 

Add all the frequencies to find the total number of data values.

 

Work out the middle position.

 

Use a cumulative frequency approach to find where this position lies in the table.

 

The data value that contains the middle position is the median.

 

If there are two middle positions, the median is the average of the two corresponding values.

 

The median depends on position, not frequency size

 

 

Finding the Mode

The mode is the value that occurs most often.

 

To find the mode:
• look for the largest frequency
• identify the corresponding data value

 

If two or more values share the highest frequency, the data set has more than one mode.

 

If all frequencies are the same, there is no mode.

 

 

Finding the Range

The range shows how spread out the data is.

 

To find the range:
• identify the smallest data value
• identify the largest data value
• subtract the smallest value from the largest value

 

Frequencies do not affect the range.

 

The range depends only on the extreme values.

 

 

Common Errors to Avoid

Common mistakes include:
• ignoring frequencies when finding the mean
• not using cumulative frequency for the median
• confusing the mode with the highest value
• using frequencies when calculating the range

 

Careful step by step methods prevent these errors.

 

 

Key Points to Remember

The mean uses data values and their frequencies.
The median is found using positions and cumulative frequency.
The mode is the value with the highest frequency.
The range is the difference between the largest and smallest values.
Frequencies must always be considered where relevant.

 

Being able to calculate the mean, median, mode and range from a discrete frequency distribution allows data to be summarised accurately and interpreted with confidence.