Chapter 3, Problem 5RE

a)

To determine

The mean and median of price in May.

Answer to Problem 5RE

Mean is 34.48 and median is 34.67.

Explanation of Solution

Given table:

May
34.54
34.62
34.35
33.67
33.72
33.27
33.49
34.59
34.98
35
34.4
34.72
35
34.84
35.47
35.67
34.96
34.78
34.99
35.59
33.16
32.72

Formula:

  $\overline{x}=\frac{{\displaystyle \sum _{i=1}^n{x}_i}}{n}$

Here n = 22 which is the count of prices.

Values of xi are price.

Calculation:

  $\overline{x}=\frac{758.53}{22}=34.48$

Mean = 34.48

To find the median, first need to sort given prices in ascending order:

May
32.72
33.16
33.27
33.49
33.67
33.72
34.35
34.4
34.54
34.59
34.62
34.72
34.78
34.84
34.96
34.98
34.99
35
35
35.47
35.59
35.67

Here n =22 which is even number.

Formula of median for even number is,

  $\begin{array}{l}Median={\left(\frac{n+1}{2}\right)}^{th}item\\ Median={\left(\frac{22+1}{2}\right)}^{th}item\\ Median={\left(11.5\right)}^{th}item\\ Median=\frac{{11}^{th}item+{12}^{th}item}{2}\\ Median=\frac{34.62+34.72}{2}\\ Median=34.67\end{array}$

b)

To determine

The mean and median of price in June.

Answer to Problem 5RE

Mean is 34.05 and median is 34.12.

Explanation of Solution

Given table:

June
34.9
35.03
34.88
35.02
34.27
34.15
34.61
34.85
35.08
34.87
34.08
33.85
33.53
33.03
32.69
32.66
32.99
33.31
33.75
33.49

Formula:

  $\overline{x}=\frac{{\displaystyle \sum _{i=1}^n{x}_i}}{n}$

Here n = 20 which is the count of prices.

Values of $x_i$ are price.

Calculation:

  $\overline{x}=\frac{681.04}{20}=34.05$

Mean = 34.05

To find the median, first need to sort given prices in ascending order:

June
32.66
32.69
32.99
33.03
33.31
33.49
33.53
33.75
33.85
34.08
34.15
34.27
34.61
34.85
34.87
34.88
34.9
35.02
35.03
35.08

Here n = 20 which is even number.

Formula of median for even number is,

  $\begin{array}{l}Median={\left(\frac{n+1}{2}\right)}^{th}item\\ Median={\left(\frac{20+1}{2}\right)}^{th}item\\ Median={\left(10.5\right)}^{th}item\end{array}$

  $\begin{array}{l}Median=\frac{{10}^{th}item+{11}^{th}item}{2}\\ Median=\frac{34.08+34.15}{2}\\ Median=34.12\end{array}$

c)

To determine

To check the difference between the price of May and June.

Answer to Problem 5RE

On an average the price of May and June are approximately same.

Explanation of Solution

Price of May:

Mean = 34.48 and median = 34.67

Price of June:

Mean = 34.05 and median = 34.12

When observing mean and median of both months, it seems they are close. There is not much difference between there mean as well as median. Hence, it can be said that both prices are approximately close.