Descriptive Statistics practice questions — SAT Math

Mean $\bar{x} = \dfrac{2 + 4 + 4 + 6}{4} = 4$.

Squared deviations: $(2-4)^{2} + (4-4)^{2} + (4-4)^{2} + (6-4)^{2} = 4 + 0 + 0 + 4 = 8$.

Variance $= \dfrac{8}{4} = 2$.

Mean: $\bar{x} = \dfrac{4+4+4+4}{4} = 4$.

All deviations are zero: $x_i - \bar{x} = 0$ for every $i$, so

$$\sigma^2 = \dfrac{1}{4}\bigl(0^2+0^2+0^2+0^2\bigr) = 0$$

Mean: $(2+4+4+6+9)/5 = 25/5 = 5$. Median (middle of the sorted set): $4$. So $m + M = 5 + 4 = 9$.

Sum $= 2 + 4 + 4 + 6 + 9 = 25$.

Mean $= \dfrac{25}{5} = 5$.

By definition, the standard deviation $\sigma$ is the square root of the variance $\sigma^2$:

$$\sigma = \sqrt{\sigma^2}$$

The mean and the sum divided by $n$ denote the arithmetic mean, not the standard deviation.

Mean: $\bar{x} = \dfrac{1+2+3}{3} = 2$.

Squared deviations:

$$(1-2)^2 + (2-2)^2 + (3-2)^2 = 1 + 0 + 1 = 2$$

So $\sigma^2 = \dfrac{2}{3}$.

With $n=3$ values:

$$\bar{x} = \dfrac{2 + 4 + 6}{3} = \dfrac{12}{3} = 4$$