The density of the earth In $1798$, the English scientist Henry Cavendish measured the density of the earth several times by careful work with a torsion balance. The variable recorded was the density of the earth as a multiple of the density of water. Here are Cavendish’s $29$ measurements:

(a) Present these measurements graphically in a stem plot.

(b) Discuss the shape, center, and spread of the distribution. Are there any outliers?

(c) What is your estimate of the density of the earth based on these measurements? Explain.

The following are the $29$measurements of the earth's density as a multiple of the density of water made by Cavendish:

The formula to compute the mean is: $Mean=\frac{Sumofobservations}{Numberofobservations}$

The stem and leaf plot is constructed as:

Because most of the data is in the center of the plot, the above-constructed plot reveals that the distribution is approximately symmetric.

Center: At the highest bar, the center has a value of $5.5$

Data has taken values ranging from $4.88$ to $5.85$

There are no values that are far apart from each other. As a result, this distribution does not contain any outliers.

The density of the earth can be estimated using the computed sample mean as follows: $$\begin{gathered} \overline{x}=\frac{\Sigma x}{n} \\ =\frac{5.50+5.61+........+5.85}{29} \\ =\frac{157.99}{29} \\ =5.4479 \end{gathered}$$

Thus, the required value is $5.4479$