Approximate the Variance and Standard Deviation of a Variable from Grouped Data
-On a recent day during the flu season, the Midtown Medical Clinic saw many patients. Patients had their temperatures taken (in °F). The distribution of temperatures is given below. Determine the standard deviation of the temperatures of a sample of 100 patients. $\begin{array}{|c|c|}
\hline \text { Temperatures } & \text { Frequency } \
\hline 95.6-96.49 & 1 \
\hline 96.5-97.39 & 3 \
\hline 97.4-98.29 & 19 \
\hline 98.3-99.19 & 28 \
\hline 99.2-100.09 & 35 \
\hline 100.1-100.99 & 12 \
\hline 101.0-101.89 & 2 \
\hline
\end{array}$

A) $1.021 ^ { \circ } \mathrm { F }$
B) $1.031 ^ { \circ } \mathrm { F }$
C) $1.015 ^ { \circ } \mathrm { F }$
D) $1.04 ^ { \circ } \mathrm { F }$

Question

Approximate the Variance and Standard Deviation of a Variable from Grouped Data
-On a recent day during the flu season, the Midtown Medical Clinic saw many patients. Patients had their temperatures taken (in °F). The distribution of temperatures is given below. Determine the standard deviation of the temperatures of a sample of 100 patients. $\begin{array}{|c|c|}
\hline \text { Temperatures } & \text { Frequency } \
\hline 95.6-96.49 & 1 \
\hline 96.5-97.39 & 3 \
\hline 97.4-98.29 & 19 \
\hline 98.3-99.19 & 28 \
\hline 99.2-100.09 & 35 \
\hline 100.1-100.99 & 12 \
\hline 101.0-101.89 & 2 \
\hline
\end{array}$

A) $1.021 ^ { \circ } \mathrm { F }$
B) $1.031 ^ { \circ } \mathrm { F }$
C) $1.015 ^ { \circ } \mathrm { F }$
D) $1.04 ^ { \circ } \mathrm { F }$

Quizplus · Accepted Answer

To approximate the standard deviation, first find the midpoint of each temperature range, then calculate the mean using these midpoints and frequencies. Next, compute the variance by finding the squared deviation of each midpoint from the mean, weighted by frequency, and divide by the total frequency minus one. Finally, take the square root of the variance to find the standard deviation, which is approximately $1.021 ^ { \circ } \mathrm { F }$.