Question

Find the mean and the standard deviation for each set of values. Show your work. 15,17,19,20,14,23,12

Answer 1

1. Mean.

$\overline{x}=\dfrac{15+17+19+20+14+23+12}{7}=\dfrac{120}{7}\approx\boxed{17.14}$

2. Standard deviation.

First we have to square each value and calculate the mean of that squares:

$\overline{x^2}=\dfrac{15^2+17^2+19^2+20^2+14^2+23^2+12^2}{7}=\boxed{\dfrac{2144}{7}}$

so the variance:

$s^2=\overline{x^2}-\overline{x}^2=\dfrac{2144}{7}-\left(\dfrac{120}{7}\right)^2\approx\boxed{12.41}$

and the standard deviation:

$s=\sqrt{s^2}=\sqrt{12.41}\approx\boxed{3.52}$