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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
1

The three averages and the range

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

The mean.
1Sum .
2Divide by 5: .
Answer6
2

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

Sum ÷ how many.
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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