Chapter 1, Problem 6CRE

a.

To determine

To show: The provided data graphically in a stem plot

Explanation of Solution

Given:

The data set is:

5.5
5.61
4.88
5.07
5.26
5.55
5.36
5.29
5.58
5.65
5.57
5.53
5.62
5.29
5.44
5.34
5.79
5.1
5.27
5.39
5.42
5.47
5.63
5.34
5.46
5.3
5.75
5.68
5.85

Formula used:

The formula to compute the mean is:

  $\text{Mean = }\frac{\text{Sum of observations}}{\text{Number of observations}}$

Graph:

The stem and leaf plot is constructed as:

  

b.

To determine

To discuss: The shape, center and shape of the distribution. Also, check if there any outliers exist.

Answer to Problem 6CRE

No.

Explanation of Solution

Calculation:

Shape: The above constructed plot shows that the distribution is approximately symmetric because most of the data is lying in the middle of the plot.

Center: The center is at the value 5.5 at the highest bar.

Spread: Data has been taking values from 4.88 to 5.85.

No values are distant away from the other values. Thus, it can be said that no outliers are present in this distribution.

c.

To determine

To find: The estimate of the density of the earth.

Answer to Problem 6CRE

The estimate is 5.4479.

Explanation of Solution

The estimate of the density of the earth can be calculated by computed sample mean as:

  $\begin{array}{c}\overline{x}=\frac{{\displaystyle \sum x}}{n}\\ =\frac{5.50+5.61+\mathrm{........}+5.85}{29}\\ =\frac{157.99}{29}\\ =5.4479\end{array}$

Thus, the required value is 5.4479.