Chapter 14.2, Problem 26E

(a)

To determine

To find: The mean, median and mode of this data.

Answer to Problem 26E

The mean median and mode are given below.

Explanation of Solution

Given:

$\begin{array}{l}\text{May}\\ \text{June}\\ \text{July}\\ \text{August}\\ \text{September}\end{array}$

$\begin{array}{l}4.8\\ 3.6\\ 3.9\\ 3.6\\ 3.7\end{array}$

Arrange the data in ascending order:

  $\left\{3.6,3.6,3.7,3.9,4.8\right\}$

The mean, median and mode are given as:

  $\begin{array}{c}\overline{x}=\frac{{\displaystyle \sum x_i}}{n}\\ =\frac{3.6+3.6+3.7+3.9+4.8}{5}\\ =3.92\\ \text{Median}=\left(\frac{5+1}{2}\right)\text{th term}\end{array}$

Further simplified as:

  $\begin{array}{c}\text{Median}=3\text{rd term}\\ =3.7\\ \text{Mode}=3.6\end{array}$

The mean median and mode are given above.

(b)

To determine

To find: The affected measure of tendency after heavy rain fall received in may totalling $8.2\text{inches}$ .

Answer to Problem 26E

The affected mean is $4.6$ .

Explanation of Solution

The mean, median and modeare calculated as:

  $\begin{array}{c}\overline{x}=\frac{{\displaystyle \sum x_i}}{n}\\ =\frac{3.6+3.6+3.7+3.9+8.2}{5}\\ =4.6\end{array}$

Further simplified as:

  $\begin{array}{c}\text{Median}=3\text{rd term}\\ =3.7\\ \text{Mode}=3.6\end{array}$

The mean would with increase in rainfall, but the median and mode would be unaffected by this change.

The affected mean, median and mode are given above.

(c)

To determine

To find: The affected measure of tendency if September is eliminated.

Answer to Problem 26E

The set of numbers is $\left\{1,2,10,10,11\right\}$ .

Explanation of Solution

The mean, median and mode are calculated as:

  $\begin{array}{c}\overline{x}=\frac{{\displaystyle \sum x_i}}{n}\\ =\frac{3.6+3.6+3.9+4.8}{4}\\ =3.97\\ \text{Median}=\frac{n}{2}\text{th term}+\left(\frac{n}{2}+1\right)\text{th term}\end{array}$

Further simplified as:

  $\begin{array}{c}\text{Median}=\frac{2\text{nd term}+3\text{rd term}}{2}\\ =\frac{3.6+3.9}{2}\\ =3.75\\ \text{Mode}=3.6\end{array}$

The mean and median would with increase in rainfall, but the mode would be unaffected by this change.

The affected mean, median and mode are given above.