Calculate the standard deviation for the heights (in centimeters) of a group of students:
160, 165, 170, 175, 180, and 185.

Given heights (in cm)

160, 165, 170, 175, 180, and 185

Calculate the Mean (Average)
Sum up all the heights and then divide by the number of heights

→ \$"Mean" = (160 + 165 + 170 + 175 + 180 + 185) / 6\$
→ \$"Mean" = 1035 / 6\$ = 172.5

The mean height is 172.5 centimeters.

Calculate the Absolute Deviations from the Mean
Find the absolute deviation of each height from the mean

\$\∣160 − 172.5\∣ = 12.5\$
\$\∣165 − 172.5\∣ = 7.5\$
\$\∣170 - 172.5\∣ = 2.5\$
\$\∣175 - 172.5\∣ = 2.5\$
\$\∣180 - 172.5\∣ = 7.5\$
\$\∣185 - 172.5\∣ = 12.5\$

Obtain the squares of each deviation

\$(12.5)^2\$ = 156.25
\$(7.5)^2\$ = 56.25
\$(2.5)^2\$ = 6.25
\$(2.5)^2\$ = 6.25
\$(7.5)^2\$ = 56.25
\$(12.5)^2\$ = 156.25

Sum up the squared deviations and then divide by the number of heights by reducing which is (n - 1) to find the mean of squared deviations

\$"Mean" = (156.25 + 56.25 + 6.25 + 6.25 + 56.25 + 156.25)/(6 - 1)\$
\$"Mean" = 437.5/5\$ = 87.5

Calculate the square root of mean of squared deviations

\$sqrt(87.5)\$

Therefore, the Standard Deviation (SD) for the heights is approximately 9.35cm.

This option is incorrect because 9.23 is not the actual standard deviation of the given data as per our caluculation

9.23

This option is correct because 9.35 matches the desired standard deviation value of the given heights in centimeters

9.35

This option is incorrect because 8.95 is close to our caluculated SD but it does not match the actual valuue as ist is slight lower

8.95

This option is incorrect because 9.56 is higher than the actual standard deviation value which is 9.35 so it is not accurate

9.56

Option

B

Can you summarize what you’ve understood in the above steps?