The mean, median, mode and range are measures used to describe a set of data. Each measure gives different information about the values in the list.

 

 

 

The Mean

The mean is the average value.

 

To find the mean:
• add all the values in the list
• divide the total by the number of values

 

The mean takes all values into account.

 

The mean can be affected strongly by very large or very small values.

 

An extreme value can pull the mean towards it

 

 

The Median

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

 

To find the median:
• write the values in ascending order

 

If there is an odd number of values:
• the median is the middle value

 

If there is an even number of values:
• the median is the mean of the two middle values

 

The median is not affected much by extreme values.

 

 

The Mode

The mode is the value that occurs most often.

 

To find the mode:
• count how many times each value appears
• identify the value with the highest frequency

 

A list can have:
• one mode
• more than one mode
• no mode

 

If all values occur the same number of times, there is no mode.

 

 

The Range

The range shows how spread out the data is.

 

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

 

The range depends only on the two extreme values.

 

Because of this, it can be affected by anomalies.

 

 

Comparing the Measures

Each measure gives different information.

 

The mean gives an overall average.
The median gives a central value.
The mode shows the most common value.
The range shows how spread out the data is.

 

Choosing the most appropriate measure depends on the context and the type of data.

 

 

Common Errors to Avoid

Common mistakes include:
• forgetting to order values before finding the median
• dividing by the wrong number when finding the mean
• confusing the mode with the median
• ignoring anomalies when interpreting the range

 

Careful organisation helps avoid these errors.

 

 

Key Points to Remember

The mean is the average of all values.
The median is the middle value when ordered.
The mode is the most frequent value.
The range measures spread using the largest and smallest values.
Different measures suit different situations.

 

Being able to calculate and interpret the mean, median, mode and range helps describe data clearly and accurately in statistics.