What is the sample variance of values 1,2,4,5

The mean is the sum of all values divided by the number of values.

$$\bar{x} = \frac{1 + 2 + 4 + 5}{4} = \frac{12}{4} = 3$$

For each value ($x_i$), subtract the mean ($\bar{x}$) and square the result.

$$(1 - 3)^2 = (-2)^2 = 4$$ $$(2 - 3)^2 = (-1)^2 = 1$$ $$(4 - 3)^2 = (1)^2 = 1$$ $$(5 - 3)^2 = (2)^2 = 4$$

Add all the squared differences from Step 2.

$$\sum (x_i - \bar{x})^2 = 4 + 1 + 1 + 4 = 10$$

The sample variance is the sum of the squared differences divided by $n-1$, where $n$ is the number of values. Here, $n=4$, so $n-1=3$.

$$s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1} = \frac{10}{3}$$ $$s^2 \approx 3.333$$

The sample variance is:

$$3.333$$