Chapter 7.3, Problem 19E

(a)

To determine

To describe:

The shape of each distribution data in a given data.

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 distribution for freshmen is symmetric and the distribution for sophomores is skewed left.

  

(b)

To determine

To explain:

The number of songs downloaded by freshmen to the number of songs downloaded sophomores.

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 $Q_{1}or{Q}_3$

The centers and spreads of the two data sets are quite different from each other.

The median for sophomores is $850$ more than the mean for freshmen.

So, sophomores is more variability in the number of songs downloaded by sophomores.

(c)

To determine

To explain:

The songs downloaded between $730\text{and}1570$ songs on $\text{MP}3$ players.

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:

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 $Q_{1}or{Q}_3$ .

Assuming a symmetric distribution is bell-shaped

  $68\%$ of the data lie within $1$ standard deviation of the mean.

Because the mean is $1150$ and the standard deviation is $420$ ,the interval from $730-1570$ represent about $68\%$ of the data.

So,expect about $0.68\left(45\right)\approx 31$ of the freshmen to have downloaded $730-1570$ songs.

(d)

To determine

To explain:

The songs downloaded between $310\text{and}1990$ songs on $\text{MP}3$ players.

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:

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 $Q_{1}or{Q}_3$ .

Assuming a symmetric distribution is bell-shaped

  $95\%$ of the data lie within $2$ standard deviation of the mean.

Because the mean is $1150$ and the standard deviation is $420$ ,the interval from $310-1990$ represent about $95\%$ of the data.

So,expect about $0.95\left(45\right)\approx 31$ of the freshmen to have downloaded $310-1990$ songs.