1

Problem

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

2

Step

Given heights (in cm):

→ 160, 165, 170, 175, 180, and 185

3

Step

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

4

Step

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\$

5

Step

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

6

Step

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

7

Step

Calculate the square root of the mean of squared deviations

\$\sqrt(87.5)\$

8

Solution

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

9

Sumup

Please summarize steps

Choices

10

Choice-A

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

Wrong 9.23

11

Choice-B

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

Correct 9.35

12

Choice-C

This option is incorrect because 8.95 is close to our calculated SD but it does not match the actual value as it is slightly lower

Wrong 8.95

13

Choice-D

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

Wrong 9.56

14

Answer

Option

B

15

Sumup

Please summarize choices