Approximate the Variance and Standard Deviation of a Variable from Grouped Data
-A 1-pound bag of peanuts contained 430 peanuts. The distribution of weights (in grams) of the peanuts is given below . What is the sample standard deviation of the weight of a peanut $\begin{array}{|l|l|}
\hline \begin{array}{l}
\text { Weights } \
\text { (grams) }
\end{array} &{\text { Frequency }} \
\hline 0.755-0.814 & 3 \
\hline 0.815-0.874 & 2 \
\hline 0.875-0.934 & 2 \
\hline 0.935-0.994 & 2 \
\hline 0.995-1.054 & 168 \
\hline 1.055-1.114 & 241 \
\hline 1.115-1.174 & 12 \
\hline
\end{array}$

A) $0.045 \mathrm {~g}$
B) $0.002 \mathrm {~g}$
C) $0.209 \mathrm {~g}$
D) $0.000004 \mathrm {~g}$

Question

Approximate the Variance and Standard Deviation of a Variable from Grouped Data
-A 1-pound bag of peanuts contained 430 peanuts. The distribution of weights (in grams) of the peanuts is given below . What is the sample standard deviation of the weight of a peanut $\begin{array}{|l|l|}
\hline \begin{array}{l}
\text { Weights } \
\text { (grams) }
\end{array} &{\text { Frequency }} \
\hline 0.755-0.814 & 3 \
\hline 0.815-0.874 & 2 \
\hline 0.875-0.934 & 2 \
\hline 0.935-0.994 & 2 \
\hline 0.995-1.054 & 168 \
\hline 1.055-1.114 & 241 \
\hline 1.115-1.174 & 12 \
\hline
\end{array}$

A) $0.045 \mathrm {~g}$
B) $0.002 \mathrm {~g}$
C) $0.209 \mathrm {~g}$
D) $0.000004 \mathrm {~g}$

Quizplus · Accepted Answer

To approximate the standard deviation, calculate the midpoint for each class, find the mean, and then use the formula for variance and standard deviation for grouped data. The correct standard deviation is approximately $0.045 \mathrm {~g}$.