What is the sample standard deviation of 1,2,4,5

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

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

Subtract the mean from each data point and square the result.

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

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

$$s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1} = \frac{10}{3} \approx 3.3333$$

The sample standard deviation is the square root of the sample variance.

$$s = \sqrt{s^2} = \sqrt{\frac{10}{3}} \approx \sqrt{3.333333} \approx 1.82574$$

Rounding to three decimal places:

$$s \approx 1.826$$

The sample standard deviation is 1.826.