For the following data set, approximate the sample standard deviation of unused vacation days . $$\begin{array} { c | c }
\text { Days } & \text { Frequency } \
\hline 1 - 2 & 9 \
3 - 4 & 22 \
5 - 6 & 28 \
7 - 8 & 15 \
9 - 10 & 14
\end{array}$$
A) 2.4 days
B) 5.5 days
C) 3.5 days
D) 5.9 days

Question

For the following data set, approximate the sample standard deviation of unused vacation days . $$\begin{array} { c | c } 
\text { Days } & \text { Frequency } \
\hline 1 - 2 & 9 \
3 - 4 & 22 \
5 - 6 & 28 \
7 - 8 & 15 \
9 - 10 & 14
\end{array}$$
A) 2.4 days
B) 5.5 days
C) 3.5 days
D) 5.9 days

Quizplus · Accepted Answer

The sample standard deviation is approximately 2.4 days. This can be calculated using the formula:s = sqrt(sum((x - mean)^2 * f) / (n - 1))where x is the midpoint of each class interval, f is the frequency of each class interval, n is the total number of observations, and mean is the sample mean.In this case, the sample mean is 4.6 days. The sample standard deviation is then calculated as:s = sqrt((9*(1.5 - 4.6)^2 + 22*(3.5 - 4.6)^2 + 28*(5.5 - 4.6)^2 + 15*(7.5 - 4.6)^2 + 14*(9.5 - 4.6)^2) / (90 - 1))= sqrt(216.6 / 89)= 2.4 days

For the Following Data Set, Approximate the Sample Standard Deviation