Chapter 1.3, Problem 99E

(a)

To determine

To explain: the shape of the distribution

Answer to Problem 99E

The shape of the distribution is right-skewed

Explanation of Solution

Given:

  

In the output we note that the mean is a lot larger than the median.

If the mean is a lot larger than the median, this indicates that the distribution is right-skewed (because the mean is influenced by large outliers, while the median remains unaffected).

(b)

To determine

To interpret: the value of the standard deviation.

Answer to Problem 99E

The value of the standard deviation is $21.6974.

Explanation of Solution

Calculation:

The value of the standard deviation (StdDev) is given in the output as:

  $s_x=21.6974$

This means that the distance between a typical amount spent by a shopper and the mean amount is $21.6974.

Conclusion:

Therefore, the value of the standard deviation is $21.6974.

(c)

To determine

To find: whether there is any outlier

Answer to Problem 99E

There might be more outliers

Explanation of Solution

Calculation:

Given in the output:

  $\begin{array}{l}{Q}_1=19.27\\ Q_3=45.4\\ Max=93.34\end{array}$

The interquartile range is the third quartile decreased by the first quartile:

  $IQR=Q_3-Q_1=45.4-19.27=26.13$

Outliers are observations that are more than 1.5 times the IQR above Q3 or below Ql.

  $\begin{array}{l}{Q}_3+1.5IQR=45.4+1.5\left(26.13\right)=84.595\\ Q_3-1.5IQR=19.27+1.5\left(26.13\right)=-19.925\end{array}$

We then note that the maximum of 93.34 is greater than 84.595 and thus the maximum is an outlier (there might be more outliers).

Conclusion:

Therefore, there might be more outliers