Data Representation and Analysis

The total is 40 and there are 5 values, so the mean is $40 \div 5 = 8$.

In order: $1, 2, 4, 5, 7, 9$. With six values there is no single middle one, so average the third and fourth: $(4+5) \div 2 = 4.5$.

$\bar{x} = 120 \div 10 = 12$. Variance $= \dfrac{1600}{10} - 12^2 = 160 - 144 = 16$, so the standard deviation is $\sqrt{16} = 4$.

$\sum fx = 2 + 12 + 24 + 16 = 54$ and $\sum f = 10$, so $\bar{x} = 5.4$.

$\sum fx^2 = 4 + 48 + 144 + 128 = 324$. Variance $= \dfrac{324}{10} - 5.4^2 = 32.4 - 29.16 = 3.24$, and $\sqrt{3.24} = 1.8$.

$Q_3 - Q_1 = 64 - 42 = 22$, and half of that is 11.