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}=(15+17+19+20+14+23+12)/(7)=(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}=(15^2+17^2+19^2+20^2+14^2+23^2+12^2)/(7)=\boxed{(2144)/(7)}`

so the variance:


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

and the standard deviation:


`s=√(s^2)=√(12.41)\approx\boxed{3.52}`