The following data represent the weekly salary of 10 people. Complete parts(a) through(e) below.

250 440 550 720 970

250 250 440 440 250

a. Obtain the sample mean and sample standard deviation of the(ungrouped) data set.

x=

sx =

(Round to one decimal place asneeded.)

b. A frequency distribution for thedata, usingsingle-value grouping, is presented in the first two columns of the following table. The third column of the table is for thexf-values. Complete the missing entries in the table and then use thegrouped-data formula to obtain the sample mean.

Salary Frequency SalaryFrequency

x f xf

250 4 1,000

440 3

500 1

720 1

970 1

Obtain the sample mean.

x=

c. Explain why thegrouped-data formula always yields the actual sample mean when the data are grouped by usingsingle-value grouping.

A.

The sum of the xf values (xifi ) for thegrouped-data is equal to the actual standard deviation

(sx).

B.

The sum of the xf values (xifi )for thegrouped-data is equal to the sum of data

(xi) for the nongrouped-data.

C.

The sum of the xf values (xifi ) for thegrouped-data is equal to the actual mean

(x).

D.

The sample means are not the same.

d. Complete thetable, then use the table and thegrouped-data formula to obtain the sample standard deviation.

Salary Frequency Deviation from mean Squared deviation SquareddeviationFrequency

x f x-x xx2 xx2f

(Round to one decimal place asneeded.)

e. Explain why thegrouped-data formula always yields the actual sample standard deviation when the data are grouped by usingsingle-value grouping.

A.

The sum of the squared deviations times the frequency

(xix2fi )for thegroup-data formula is equal to the actual sample standard deviation (sx).

B.

The sum of the squared deviations times the frequency

(xix2 )fi for thegroup-data formula is equal to the sample mean of the data (x).

C.

The sum of the squared deviations times the frequency

(xix2fi )for thegroup-data formula is equal to the sum of the squared deviations xix2

for the nongrouped-data.

D.

The two sample standard deviations are different.