To find the sample standard deviation of the blood pressures for the younger adults, we need to follow these steps:
- Calculate the mean (average) of the data set.
- Subtract the mean from each data point and square the result.
- Sum all the squared results.
- Divide this sum by the number of data points minus one (this is the variance).
- Take the square root of the variance to get the standard deviation.
Let's go through these steps with the given data for younger adults: 110, 101, 92, 121, 101, 121, 121, 120, 112, 109.
\[
\text{Mean} = \frac{110 + 101 + 92 + 121 + 101 + 121 + 121 + 120 + 112 + 109}{10} = \frac{1108}{10} = 110.8
\]
\[
(110 - 110.8)^2 = (-0.8)^2 = 0.64
\]
\[
(101 - 110.8)^2 = (-9.8)^2 = 96.04
\]
\[
(92 - 110.8)^2 = (-18.8)^2 = 353.44
\]
\[
(121 - 110.8)^2 = (10.2)^2 = 104.04
\]
\[
(101 - 110.8)^2 = (-9.8)^2 = 96.04
\]
\[
(121 - 110.8)^2 = (10.2)^2 = 104.04
\]
\[
(121 - 110.8)^2 = (10.2)^2 = 104.04
\]
\[
(120 - 110.8)^2 = (9.2)^2 = 84.64
\]
\[
(112 - 110.8)^2 = (1.2)^2 = 1.44
\]
\[
(109 - 110.8)^2 = (-1.8)^2 = 3.24
\]
\[
0.64 + 96.04 + 353.44 + 104.04 + 96.04 + 104.04 + 104.04 + 84.64 + 1.44 + 3.24 = 947.6
\]
\[
\text{Variance} = \frac{947.6}{10 - 1} = \frac{947.6}{9} \approx 105.29
\]
\[
\text{Standard Deviation} = \sqrt{105.29} \approx 10.26
\]
So, the sample standard deviation of the blood pressures for the younger adults is approximately 10.3 (rounded to one decimal place).