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4.2 Representing data

Averages and spread

Everything on averages and spread that can come up in the WJEC GCSE Mathematics and Numeracy, in all three units. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.

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A worked example

Averages · [1 mark]

Here are the marks in a quiz: 23, 25, 26, 25, 25, 26, 25, 23, 25. Find the range.

  1. B126 − 23: 3

The exam skills (6)

Averages

  1. Mean: add them all up, divide by how many there are.
  2. Median: put them in order and find the middle one.
  3. Mode: the most common. Range: biggest − smallest.

Watch out: Finding the median without putting the numbers in order first.

Worked example · Practise this skill free

Mean from a table

  1. Multiply each value by its frequency.
  2. Add those up to get the total.
  3. Divide by the total frequency (not the number of rows).

Watch out: Dividing by the number of rows in the table.

Worked example · Practise this skill free

Estimating the mean

  1. Find the midpoint of each group.
  2. Multiply each midpoint by its frequency and add them up.
  3. Divide by the total frequency. It is an estimate because you used midpoints.

Watch out: Using the end of each group instead of the midpoint.

Worked example · Practise this skill free

Modal and median class

  1. Modal class: the group with the highest frequency.
  2. Median position: (n + 1) ÷ 2.
  3. Add the frequencies down the table until you pass that position: that group holds the median.

Watch out: Picking the middle row of the table as the median class.

Worked example · Practise this skill free

Combined mean

  1. Turn each mean back into a total: mean × number.
  2. Add the totals together.
  3. Divide by the total number of people.

Watch out: Averaging the two means. That only works if the groups are the same size.

Worked example · Practise this skill free

Histograms

  1. Frequency density = frequency ÷ class width.
  2. So frequency = frequency density × class width.
  3. Class width = top of the group − bottom.

Watch out: Reading the height of the bar as the frequency. In a histogram, area is frequency.

Worked example · Practise this skill free

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