S1StatisticsFoundation

Averages & Range

An average is a single number that represents a whole set of data. There are three — mean, median and mode — plus the range, which measures how spread out the data is.

35 min Video by Maths Genie AQA GCSE Maths

Finding the Mean, Median, Mode and RangeWatch the walkthrough, then read the notes below.

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What you'll learn

Find the mean, median and mode
Find the range
Choose the best average
Find a missing value given the mean

The three averages and the range

$Mean$ : add up all the values and divide by how many there are. $Median$ : the middle value when in order. $Mode$ : the most common value. $Range$ : largest minus smallest.

mean = \frac{sum of values}{number of values}

The mean.

1Sum

= 4 + 7 + 9 + 4 + 6 = 30

2Divide by 5:

30 \div 5 = 6

Answer6

Choosing and using averages

The median is best when there are extreme values; the mode is the only average for non-numerical data. To find a missing number from the mean, multiply the mean by how many values there are to get the total, then subtract.

Tip — Put the data in order before finding the median — a very common slip.

Remember these

mean = \frac{\sum x}{n}

Sum ÷ how many.

range = max - min

Spread of the data.

Watch out for these

Finding the median without ordering the data first.

Always sort smallest to largest before taking the middle.

Confusing the range with an average.

The range measures spread, not a typical value.

Key takeaways

Mean = sum ÷ number; median = middle (in order); mode = most common.
Range = largest − smallest.
Median is best with extreme values.

Test yourself

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