Provide an Appropriate Response $\begin{array} { r r r r r r } 280 & 320 & 590 & 320 & 730 & 590 \\ 320 & 590 & 280 & 320 & 1150 & 280 \end{array}$

Multiple Choice

Provide an appropriate response.
-A company's raw-data sample of weekly salaries (in dollars) is shown below.
$\begin{array} { r r r r r r } 280 & 320 & 590 & 320 & 730 & 590 \\ 320 & 590 & 280 & 320 & 1150 & 280 \end{array}$
A frequency distribution of this data set, based on single-value grouping, is presented below, with a third column showing the xf-values--the class midpoint (which here is the same as the class) times the class frequency.
$\begin{array}{|l|l|l|}\hline \begin{array}{l}\text { Salary } \\x\end{array} & \begin{array}{l}\text { Frequency } \\\text { f }\end{array} & \begin{array}{l}\text { Salary }{ }^{*} \text { Frequency } \\x f\end{array} \\\hline 280 & 3 & 840 \\320 & 4 & 1280 \\590 & 3 & 1770 \\730 & 1 & 730 \\1150 & 1 & 1150 \\\hline\end{array}$

A) (i) Use the raw data to obtain the sample standard deviation of the ungrouped data. Round your answer to two decimal places.
(ii) Use the grouped-data formula to obtain the sample standard deviation of the grouped data in
The frequency distribution. Round your answer to two decimal places.
(iii) Compare your answers in parts (i) and (ii) . (i) The sample standard deviation of the ungrouped data is 264.59; (ii) The sample standard deviation of the grouped data is 264.59;
(iii) The results in parts (i) and (ii) are the same. The grouped data formula will always Provide the actual standard deviation when the data are grouped in classes each based on a Single value because the class midpoint is the same as each observation in each class.
B) (i) The sample standard deviation of the ungrouped data is 286.28; (ii) The sample standard deviation of the grouped data is 286.28;
(iii) The results in parts (i) and (ii) are the same. The grouped data formula will always Provide the actual standard deviation when the data are grouped in classes each based on a Single value because the class midpoint is the same as each observation in each class.
C) (i) The sample standard deviation of the ungrouped data is 264.59; (ii) The sample standard deviation of the grouped data is 286.28;
(iii) The results in parts (i) and (ii) are different. This discrepancy occurs because in the Grouped data formulas, every actual data value in a given class is replaced by the class Midpoint even though most values in the class are not equal to the midpoint.
D) (i) The sample standard deviation of the ungrouped data is 286.28; (ii) The sample standard deviation of the grouped data is 299.01;
(iii) The results in parts (i) and (ii) are different. This discrepancy occurs because in the Grouped data formulas, every actual data value in a given class is replaced by the class Midpoint even though most values in the class are not equal to the midpoint.