Question

question for the following set of data, find the number of data within 1 population standard deviation of the mean. 61, 61, 60, 71, 65, 57, 60 answer attempt 1 out of 2

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{61 + 61+60 + 71+65+57+60}{7}=\frac{435}{7}\approx62.14$

Step2: Calculate the population - variance

First, find the squared - differences from the mean:
$(61 - 62.14)^2\approx1.3$; $(61 - 62.14)^2\approx1.3$; $(60 - 62.14)^2\approx4.6$; $(71 - 62.14)^2\approx78.5$; $(65 - 62.14)^2\approx8.2$; $(57 - 62.14)^2\approx26.4$; $(60 - 62.14)^2\approx4.6$
The population variance $\sigma^{2}=\frac{1.3 + 1.3+4.6+78.5+8.2+26.4+4.6}{7}=\frac{124.9}{7}\approx17.84$

Step3: Calculate the population standard - deviation

$\sigma=\sqrt{17.84}\approx4.22$

Step4: Find the range within 1 standard - deviation of the mean

The lower bound is $62.14−4.22 = 57.92$ and the upper bound is $62.14 + 4.22=66.36$

Step5: Count the number of data within the range

The data values $61,61,60,65,60$ are within the range. So there are 5 data values within 1 population standard - deviation of the mean.

Answer:

5