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.

Given weights (in grams)

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

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

The mean weight is 52.85 grams.

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

\$\∣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\$

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

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

calculate the square root of mean of squared deviations

\$sqrt(656.44)\$

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

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

25.61

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

25.09

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

24.98

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

24.37

Option

A

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