1

Problem

Calculate the standard deviation for the sample weights (in grams): 62.3, 74.1, 51.8, 23.5, 25.2, 40.9, and 93.2.

2

Step

Given weights (in grams):

62.3, 74.1, 51.8, 23.5, 25.2, 40.9, and 93.2

3

Step

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

\$Mean = (62.3 + 74.1 + 51.8 + 23.5 + 25.2 + 40.9 + 93.2) / 7\$

\$Mean = (371) / 7\$ = 53

4

Step

Calculate the Absolute Deviations from the Mean: The absolute deviation of each weight from the mean is

\$\∣62.3 − 53\∣ = 9.3\$
\$\∣74.1 - 53\∣ = 21.1\$
\$\∣51.8 - 53\∣ = 1.2\$
\$\∣23.5 - 53\∣ = 29.5 \$
\$\∣25.2 - 53\∣ = 27.8\$
\$\∣40.9 - .53\∣ = 12.1\$
\$\∣93.2 -.53\∣ = 40.2\$

5

Step

Obtain the squares of each deviation:

\$9.3^2\$ = 86.49

\$21.1^2\$ = 445.21

\$1.2^2\$ = 1.44

\$29.5^2\$ = 870.25

\$27.8^2\$ = 772.84

\$12.1^2\$ = 146.41

\$40.2^2\$ = 1616.04

6

Step

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

\$Mean = (86.49 + 445.21 + 1.44 + 870.25 + 772.84 + 146.41 + 1616.040) / (7 - 1)\$

\$Mean = (3938.68) / 6\$ = 656.44

7

Step

Calculate the square root of the mean of squared deviations:

\$\sqrt(656.44)\$

8

Solution

Therefore, the Standard Deviation (SD) for the weights is approximately 25.61cm.

9

Sumup

Please summarize steps

Choices

10

Choice-A

This option is correct because 25.61 is the accurate standard deviation of the given weights in grams

Correct 25.62

11

Choice-B

This option is incorrect but, 25.09 is closer to the actual result of the given weights but it is not accurate SD which is 25.61 grams

Wrong 25.09

12

Choice-C

This option is incorrect because 24.98 is slightly lower than the actual standard deviation of the given weights in grams

Wrong 24.98

13

Choice-D

This option is incorrect because 24.37 does not match the actual standard deviation of the given data

Wrong 24.37

14

Answer

Option

A

15

Sumup

Please summarize choices