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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

For the following set of data, find the number of data within 2 population standarddeviations-example-1
User Nakia
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6 votes

Answer:

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:


\begin{gathered} \operatorname{mean}\text{ = }(87+63+39+67+66+63+62+67+66)/(9) \\ \operatorname{mean}\text{ = }(580)/(9) \\ \operatorname{mean}\text{ = 64.44} \end{gathered}

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.

User Ulentini
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