Chapter 7.3, Problem 10E

(a)

To determine

To explain:

The data in a histogram using five intervals.

Explanation of Solution

Given:

Each entry in a two −way table

Concept used:

Bivariate joint frequency distribution are contingency table.

The total row and total column of the marginal distribution while the body of the table is the joint frequencies

Calculation:

The most data are the five-number summary because the median is closer to either $Q_{1}or{Q}_3$

Standard deviation is the variation from the mean.

Prepare a frequency table with $6$ intervals

IQ scores	Frequency
$151-166$	$3$
$167-182$	$8$
$183-198$	$4$
$199-214$	$1$
$215-230$	$2$

(b)

To determine

To explain:

The measures of center and variation best represent the data in a histogram using five intervals.

Explanation of Solution

Given:

Each entry in a two −way table

Concept used:

Bivariate joint frequency distribution are contingency table.

The total row and total column of the marginal distribution while the body of the table is the joint frequencies

Calculation:

The most data are the five-number summary because the median is closer to either $Q_{1}or{Q}_3$

Standard deviation is the variation from the mean.

Prepare a frequency table with $6$ intervals

IQ scores	Frequency
$151-166$	$3$
$167-182$	$8$
$183-198$	$4$
$199-214$	$1$
$215-230$	$2$

The measures of center and variation best represent the data in a histogram.

Because most of the data are on the left and the tail of the graph extends to the right the distribution is skewed right.

Therefore use the median to the center and five-number summary to the variation.

(c)

To determine

To explain:

The distribution of IQ scores for the human population is symmetric and shape of the distribution in a histogram using five intervals.

Explanation of Solution

Given:

Each entry in a two −way table

Concept used:

Bivariate joint frequency distribution are contingency table.

The total row and total column of the marginal distribution while the body of the table is the joint frequencies

Calculation:

The most data are the five-number summary because the median is closer to either $Q_{1}or{Q}_3$

Standard deviation is the variation from the mean.

Prepare a frequency table with $6$ intervals

IQ scores	Frequency
$151-166$	$3$
$167-182$	$8$
$183-198$	$4$
$199-214$	$1$
$215-230$	$2$

For symmetric distribution :-the mean corresponds to half of the data on $Q_2$ and the

Standard deviation is the variation from the mean.

For skewed distribution :-the median corresponds to most likely lie

The most data are the five-number summary because the median is closer to either $Q_{1}or{Q}_3$

Therefore the shape of the distribution become symmetric.