Question

Compare the three data sets on the right.

​(i)

45678910 A dot plot has a horizontal axis labeled from 4 to 10 in increments of 1. The graph consists of a series of plotted points from left to right. The coordinates of the plotted points are as follows, where the label is listed first and the number of dots is listed second: 5, 1; 6, 4; 7, 5; 8, 4; 9, 1.

​(ii)

45678910 A dot plot has a horizontal axis labeled from 4 to 10 in increments of 1. The graph consists of a series of plotted points from left to right. The coordinates of the plotted points are as follows, where the label is listed first and the number of dots is listed second: 5, 2; 6, 3; 7, 5; 8, 3; 9, 2.

​(iii)

45678910 A dot plot has a horizontal axis labeled from 4 to 10 in increments of 1. The graph consists of a series of plotted points from left to right. The coordinates of the plotted points are as follows, where the label is listed first and the number of dots is listed second: 6, 4; 7, 7; 8, 4.

​(a) Which data set has the greatest sample standard​ deviation?

A.Data set

left parenthesis ii right parenthesis(ii)​,

because it has more entries that are farther away from the mean.

B.Data set

left parenthesis i right parenthesis(i)​,

because it has two entries that are far away from the mean.

C.Data set

left parenthesis iii right parenthesis(iii)​,

because it has more entries that are close to the mean.

Which data set has the least sample standard​ deviation?

A.Data set

left parenthesis i right parenthesis(i)​,

because it has less entries that are farther away from the mean.

B.Data set

left parenthesis iii right parenthesis(iii)​,

because it has more entries that are close to the mean.

C.Data set

left parenthesis ii right parenthesis(ii)​,

because it has more entries that are farther away from the mean.

​(b) How are the data sets the​ same? How do they​ differ?

A.

The three data sets have the same mean and mode but have different medians and standard deviations.

B.

The three data sets have the same standard deviations but have different means.

C.

The three data sets have the same mode but have different standard deviations and means.

D.

The three data sets have the same​ mean, median and mode but have different standard deviations.

Click to select your answer.

Answer 1

Descriptive Statistics: (i), (ii), (iii)

N for
Variable Mean StDev Median Mode Mode
(i) 7.000 1.069 7.000 7 5
(ii) 7.000 1.254 7.000 7 5
(iii) 7.000 0.756 7.000 7 7

(a)

A.Data set

left parenthesis ii right parenthesis(ii)​,

because it has more entries that are farther away from the mean.

B.Data set

left parenthesis iii right parenthesis(iii)​,

because it has more entries that are close to the mean.

(b)

D.

The three data sets have the same​ mean, median and mode but have different standard deviations.