Rukasha Maths

GCSE maths Beta

Averages, frequency tables and range · Revision guide

Foundation · Statistics · 1 page in the PDF

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Learning objectives

  • Calculate mean, median, mode and range.
  • Find a mean from a frequency table.

Key ideas

The mean uses every value, including repetitions.

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

Order values for the median. For an even count, average the two middle values.

The mode is the most frequent value. There may be several modes or no unique mode.

Range measures the spread between the extremes.

range=maximum−minimum\text{range}=\text{maximum}-\text{minimum}

For a frequency table, multiply each value by its frequency before adding.

mean=∑xf∑f\text{mean}=\frac{\sum xf}{\sum f}

Worked examples

Example 1

Books read are zero, one and two, with respective frequencies two, three and five. Find the mean.

∑xf=0(2)+1(3)+2(5)=13\sum xf=0(2)+1(3)+2(5)=13
∑f=2+3+5=10\sum f=2+3+5=10
mean=1310=1.3 books\text{mean}=\frac{13}{10}=1.3\text{ books}
1.3 books1.3\text{ books}

Example 2

Find the median of the six given values.

Order the values.

9,2,6,3,8,4⟶2,3,4,6,8,99,2,6,3,8,4\quad\longrightarrow\quad2,3,4,6,8,9
median=4+62=5\text{median}=\frac{4+6}{2}=5
55

Watch out

A frequency counts repetitions. Do not divide a frequency-table total by the number of distinct values.