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.)

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

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 $={\displaystyle \frac{4+5}{2}}=4.5$.

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

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

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 $=22-4=18$.