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, 66

Answer 1

8

Step-by-step explanation:

First, we need to find the mean, so the sum of all values divided by the number of values is equal to:

Then, we need to find the population standard deviation, so we need to find the square of the difference between each value and the mean:

(87 - 64.44)² = 508.75

(63 - 64.44)² = 2.08

(39 - 64.44)² = 647.41

(67 - 64.44)² = 6.53

(66 - 64.44)² = 2.41

(63 - 64.44)² = 2.08

(62 - 64.44)² = 5.97

(67 - 64.44)² = 6.53

(66 - 64.44)² =2.41

Now, the standard deviation will be the square root of the sum of these values divided by the number of values, so:

`\begin{gathered} s=\sqrt[]{(508.75+2.08+647.41+6.53+2.41+2.08+5.97+6.53+2.41)/(9)} \\ s=\sqrt[]{(1184.22)/(9)} \\ s=\sqrt[]{131.58} \\ s=11.47 \end{gathered}`

Therefore, the data that is within 2 population standard deviations to the mean is the data that is located within the following limits:

mean + 2s = 64.44 + 2(11.47) = 87.38

mean - 2s = 64.44 - 2(11.47) = 41.5

So, from the 9 values, 8 are within 2 population standard deviations of the mean.

Therefore, the answer is 8.