Chapter 2, Problem 2.1AYK

(a)

To determine

To construct: the dot plot for the given data and comment about the shape, center and spread of the data.

Answer to Problem 2.1AYK

Shape = Right skewed

Center = 290

Explanation of Solution

Given:

164	478.7	251.3	351.7	173	448.9	300.6
362	272.4	740.2	329	327.2	270.5	332.1
288.8	176.1	282.2	236.1	358.2	270.5	290.7

Calculations:

The dot plot for the given dataset:

  

The shape of the given data is Right skewed, center of the data is 290.

(b)

To determine

To calculate: the mean and medina for the given data and compare it with the dot plot’s center.

Answer to Problem 2.1AYK

Mean = 319.25

Median = 290.7

Explanation of Solution

Formula used:

  $\begin{array}{l}\text{Mean = }\frac{\sum x_i}{n}\\ \text{Median = }\left\{\begin{array}{l}{\left(\frac{\text{n + 1}}{2}\right)}^{\text{Th tern}},\text{When n is odd}\\ \frac{{\left(\frac{n}{2}\right)}^{\text{Th term}}+{\left(\frac{n}{2}+1\right)}^{\text{Th term}}}{2},\text{When n is even}\end{array}\right\}\end{array}$

Calculation:

  $\begin{array}{c}\text{Mean = }\frac{6704.2}{21}\\ =319.25\end{array}$

  $\begin{array}{c}\text{Median = }{\left(\frac{21+1}{2}\right)}^{\text{Th term}}\\ ={11}^{\text{Th term}}\\ =290.7\end{array}$

The center value based on the dot plot is near to 290 and the center value median is 290.7, they are almost the same. The mean value of the data is 319.25.

The median is considered as the best measure of central tendency because the data is right skewed and when the data is skewed then median is considered best as it does not get affected by the extreme values.