Chapter 4, Problem 33E

(a)

To determine

To find: the measure of centre and spread are the most appropriate.

Explanation of Solution

Given:

  

State populations (1|2 means 12 million)

By seeing the stem plot, it is observed that there is not symmetric and it is skewed to right. Therefore the best measure of centre is by median and with median the best measure of spread is inter quartile range. Therefore the on the basis of given distribution median as the measure of centre and IQR as the measure of spread are the most suitable.

(b)

To determine

To find: the larger the median or mean.

Explanation of Solution

Given:

  

By seeing the distribution, it is observed that the distribution is skewed to right then the mean is greater than median and if the distribution is left skewed then the mean is smaller than the median. This is highly skewed to right distribution so the mean is larger than the median. For the skewed distribution the median is more suitable than mean.

(c)

To determine

To find: the median and the inter quartile range from the given stem and leaf plot.

Explanation of Solution

Given:

  

Middle value of the ordered data in known as median and 51 is the total number of states so the median would be (50/2+1=26^th value) by seeing the stem plot 26^th value is 4 million so the median is 4 million.

Middle value of lower half of the data set is lower quartile and the upper quartile is the middle value of upper half of data set.

For the lower half of the data is 26. Average value of 13^th position which is 1 million and 14^th position which is 2 million of lower half of the data list is lower quartile.

  $Q_1=1.5million$

Similarly for upper half

  $Q_3=6million$

  $\begin{array}{c}IQR=Q_3-Q_1\\ =6-1.5\\ =4.5million\end{array}$

So the inter quartile range is 4.5 million

(d)

To determine

To Explain: the distribution few sentences.

Explanation of Solution

Given:

  

By seeing the stem plot, it seems that the distribution is not symmetric. It is skewed to right, unimodal and mode is in stem is 0 which is the lowest. Median of the distribution is the 4 million. There is one outlier in the distribution. There is only one state which has the 34 million populations.