Averages and range: solved examples

Worked examples of averages and range, from easy to hard, with every step written out. Try each one yourself first, then check the working.

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Easy

Example 1. Find the range of: 9, 28, 16, 21, 9, 8
1. Subtract the smallest from the largest. $28 - 8 = 20$
Answer: $20$
Example 2. Find the mode of: 24, 18, 24, 8, 1, 26
1. 24 appears twice; every other value appears once. $\text{mode} = 24$
Answer: $24$
Example 3. Find the mode of: 3, 4, 25, 3, 16, 17
1. 3 appears twice; every other value appears once. $\text{mode} = 3$
Answer: $3$

Example 4. Find the median of: 12, 38, 21, 27, 12, 11, 17
1. Order the data. $11,\ 12,\ 12,\ 17,\ 21,\ 27,\ 38$
2. Find the middle. $\text{median} = 17$
Answer: $17$
Example 5. Find the mean of: 11, 5, 34, 12, 35
1. Add the values. $\text{total} = 97$
2. Divide by 5. $\frac{97}{5} = \frac{97}{5}$
Answer: $\frac{97}{5}$
Example 6. Find the mean of: 37, 1, 39, 18, 4, 7, 25
1. Add the values. $\text{total} = 131$
2. Divide by 7. $\frac{131}{7} = \frac{131}{7}$
Answer: $\frac{131}{7}$

Example 7. Find the mean of: 12, 38, 21, 27, 12, 11, 17, 14
1. Add the values. $\text{total} = 152$
2. Divide by 8. $\frac{152}{8} = 19$
Answer: $19$
Example 8. Find the mean of: 11, 5, 34, 12, 35, 32
1. Add the values. $\text{total} = 129$
2. Divide by 6. $\frac{129}{6} = \frac{43}{2}$
Answer: $\frac{43}{2}$
Example 9. Find the median of: 37, 1, 39, 18, 4, 7, 25, 36
1. Order the data. $1,\ 4,\ 7,\ 18,\ 25,\ 36,\ 37,\ 39$
2. Find the middle. $\text{median} = \frac{43}{2}$
Answer: $\frac{43}{2}$

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