Descriptive Statistics & Sampling practice questions — GCSE Maths

Sorted: $\{1, 3, 5, 7, 9\}$. The middle value (3rd of 5) is $5$.

Add every value in the set.

$$6+8+11+15+20 = 60$$

Divide the total by the count of numbers, which is $5$.

$$\frac{60}{5} = 12$$

The mean is $12$. (Note $11$ is the median and $14$ is the range — different measures.)

Add up all five values: $$3+3+4+6+9=25$$ Divide the total by the number of matches: $$\frac{25}{5}=5$$ So the mean is $5$ goals per match. (Here $4$ is the median, $3$ is the mode, and $6$ is the range.)

$\dfrac{2 + 4 + 6 + 8 + 10}{5} = \dfrac{30}{5} = 6$.

The value appearing most often is $5$ (three times).

Sorted: $\{1, 3, 4, 5, 6, 8\}$. The two middle values are $4$ and $5$. Median $= \dfrac{4 + 5}{2} = 4.5$.

Sum $= 40$, $n = 8$, so $\bar{x} = 5$. Squared deviations: $9, 1, 1, 1, 0, 0, 4, 16$ — sum $= 32$. Variance $= \dfrac{32}{8} = 4$.

Sum $= 5 \cdot 7 + 8 \cdot 8 + 7 \cdot 9 = 35 + 64 + 63 = 162$. Mean $= \dfrac{162}{20} = 8.1$.

Sorted (already): $\{2, 4, 5, 7, 8, 11, 14\}$. Median is $7$ (position 4). Lower half: $\{2, 4, 5\}$. Median of lower half: $4$. So $Q_1 = 4$.

Max $= 22$, min $= 4$, so range $= 22 - 4 = 18$.