Question

101, 102, 100, 100, 110, 109, 109, 108, 109
d. Find the variance of the data.
e. Find the standard deviation of the data.

Answer 1

ill help you

Answer 2

thank you @prowrestler

Answer 3

For the variance of the data you need first the mean value of the data,
\[\overline{x}=(101+ 102+ 100+ 100+ 110+ 109+ 109+ 108+ 109)/9\] As you know, the sum of all values, divided by the number of values. Once you get this, the variance can be calculated with this formula,
\[Var=\frac{\sum_i(x_i-\overline{x})^2}{N}\] Where x_i is each data, N the number of data, and the overlined x is the mean.

For the standard deviation,
\[\sigma=\sqrt{Var}\]

Answer 4

I dont understand... @John_ES

Answer 5

First, do you understand how to calculate the mean?

Answer 6

When you calculate the mean value of your data, you will obtain this,
\[\overline{x}=(101 + 102 + 100 + 100 + 110 + 109 + 109 + 108 + 109)/9=316/3\\
\overline{x}\approx105.3\]

Answer 7

yes, but I dont know how to use this Var=∑i(xi−x¯)2N @John_ES

Answer 8

Ok, I will expand the formula using your data

Answer 9

\[Var=((101-105.3)^2+(102-105.3)^2+2\cdot(100-105.3)^2+\\
+(108-105.3)^2+3\cdot(109-105.3)^2+(110-105.3)^2)/9\]

Answer 10

Ok, then,
\[Var\approx17.33\] And
\[\sigma\approx\sqrt{Var}=4.16\]

Answer 11

Only for checking.