Solve any maths problem

Step by step

1. 1, 2, 3, 4, 5

   5 values.

2. \bar{x} = \frac{1 + 2 + 3 + 4 + 5}{5} = \frac{15}{5} = 3

   Mean: add them up and divide by how many there are.

3. (1 - 3)^2 = 4 ,\; (2 - 3)^2 = 1 ,\; (3 - 3)^2 = 0 ,\; (4 - 3)^2 = 1 ,\; (5 - 3)^2 = 4

   Squared deviations from the mean.

4. \sigma^2 = \frac{\sum (x_i - \bar x)^2}{n} = 2

   Population variance (divide by n).

5. s^2 = \frac{\sum (x_i - \bar x)^2}{n - 1} = \frac{5}{2}

   Sample variance (divide by n − 1).

6. \sigma = \sqrt{2} = \sqrt{2} \approx 1.4142,\quad s = \frac{\sqrt{10}}{2} \approx 1.5811

   Standard deviation is the square root of the variance.