Question

For the following set of data, find the number of data within 2 population standarddeviations of the mean.87, 63, 39, 67, 66, 63, 62, 67, 66Copy Values for CalculatorOpen Statistics Calculator

Answer 1

We have to calculate the number of data within 2 population standard deviation of the mean.

For we have to find the mean of the given data.

Mean is given by

$\operatorname{mean}=\frac{87+63+39+67+66+63+62+67+66}{9}=\frac{580}{9}=64.44$

The standard deviation is given by the formula,

$\sigma=\sqrt[]{\frac{\Sigma(x_i-\operatorname{mean})^2}{9}}$

Then the standard deviation is given by

$\sigma^2=\frac{(87-64.4)^2+\cdots+(66-64.4)^2^{}}{9}=\frac{1184.22}{9}=131.58$

Hence the standard deviation is

$\sigma=\sqrt[]{131.58}=11.47$