Statistics · Ordinary Level
The Mean & Spread
Ordinary Level · Class 3 · Tap NEXT to begin
Section 1 of 2
Working with the Mean
Total = mean × how many
Rearrange the mean: total $=$ mean $\times$ how many. That solves missing-value and combined-mean questions.
Worked example — missing value
$2, 5, 3, x, 10$ have a mean of $6$. Find $x$.
Total $= 6 \times 5 = 30$; known sum $= 20$
$x = 30 - 20 = 10$
$x = 10$
Worked example — missing value
$2, 7, 3, x, 9, 11$ have a mean of $8$. Find $x$.
Total $= 6 \times 8 = 48$; known sum $= 32$
$x = 48 - 32 = 16$
$x = 16$
Combined means
You can’t average two means. Find each group’s total (mean $\times$ size), add, divide by the total number.
Worked example — two groups of games
In $5$ games the mean was $2$ goals; in $4$ games the mean was $2.5$. Find the mean over all $9$ games.
$5 \times 2 = 10$; $4 \times 2.5 = 10$; total $= 20$
$\bar{x} = \tfrac{20}{9}$
$\tfrac{20}{9} \approx 2.2$
Worked example — girls and boys
$6$ girls have mean age $10$; $9$ boys have mean age $12$. Find the mean age of all $15$.
$6 \times 10 = 60$; $9 \times 12 = 108$; total $= 168$
$\bar{x} = \tfrac{168}{15} = 11.2$
$11.2$
Section 2 of 2
The Spread — Range & IQR
Two measures
Range $=$ highest $-$ lowest. IQR $=$ upper quartile $-$ lower quartile (the middles of the upper and lower halves).
Worked example — range and IQR
Find the range and interquartile range of $2, 3, 5, 7, 8, 10, 15$.
Range $= 15 - 2 = 13$
Median $7$; lower quartile $3$, upper quartile $10$
IQR $= 10 - 3 = 7$
range $13$, IQR $7$
Worked example — another
Find the range and interquartile range of $2, 9, 3, 4, 6, 8, 11$.
Order $2,3,4,6,8,9,11$; range $= 11 - 2 = 9$
Lower quartile $3$, upper quartile $9$
IQR $= 9 - 3 = 6$
range $9$, IQR $6$
You try
Find the mode, median, mean, range and IQR of $3, 5, 1, 1, 7, 8, 12$.
Order first: $1,1,3,5,7,8,12$.
Mode $= 1$; median $= 5$ (the $4$th); mean $= \tfrac{37}{7}$
Range $= 12 - 1 = 11$; lower quartile $1$, upper quartile $8$, IQR $= 7$
mode $1$, median $5$, mean $\tfrac{37}{7}$, range $11$, IQR $7$
That’s Class 3.
Total $=$ mean $\times$ how many, combined means, range and interquartile range. Class 4: frequency tables.