Mean, median, mode and range

Calculating the mean, median, mode and range, finding a missing value from the mean, the effect of outliers and choosing the best measure.

The measures

Example 1●

Find the mean, median, mode and range of $4, 7, 7, 9, 13$.

Mean $= 40 \div 5 = 8$

Median $= 7$, mode $= 7$, range $= 13 - 4 = 9$

Example 2●●

The mean of five scores is $12$. Four of them are $10, 14, 9, 15$. Find the fifth.

Total $= 5 \times 12 = 60$

Fifth $= 60 - 48 = 12$

Flashcards

Median of $3, 5, 8, 10$

$6.5$

Missing value from a mean

Total $=$ mean $\times$ count, then subtract.

Measure least affected by outliers

Median

Practice

Find the mean of $4, 7, 7, 9, 13$.
The mean of five scores is $12$. Four are $10, 14, 9, 15$. Find the fifth.
Find the median of $3, 5, 8, 10$.
Find the range of $4, 7, 7, 9, 13$.
Find the mode of $1, 2, 2, 3, 4, 2, 5$.
Find the median of $8, 2, 5, 9, 1$.
Salaries in a small company are $\$50$k, $\$55$k, $\$60$k and $\$500$k. Which measure best describes a typical salary?
Five numbers have mean $10$. A sixth number is added and the mean becomes $11$. What is the sixth number?