Question

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 bal- ance. The variable recorded was the density of the earth as a multiple of the density of water. Here are .51 Cavendish's 29 measurements: 5.50 5.61 4.88 5.07 5.26 5.55 5.36 5.295.58 5.65 5.57 5.53 5.62 5.29 5.44 5.34 5.79 5.10 5.27 5.39 5.42 5.47 5.63 5.34 5.46 5.30 5.75 5.68 5.85 (a) Present these measurements graphically in a stemplot. (b) Discuss the shape, center, and spread of the distri- bution. Are there any outliers? (c) What is your estimate of the density of the earth based on these measurements? Explain.

Answer 1

Answer: a) To present the measurements graphically in a stemplot, we first need to separate each measurement into a stem and a leaf. The stem represents the whole number part, and the leaf represents the decimal part. Here is the stemplot:

4 | 8

5 | 001022233344445556677899

The stemplot shows the frequency of each measurement. For example, there are two measurements with a stem of 5 and a leaf of 0, one measurement with a stem of 5 and a leaf of 1, and so on.

(b) From the stemplot, we can observe the following:

- Shape: The stemplot shows a unimodal shape, with a slight skewness to the right. This means that most of the measurements cluster around the center, but there are a few larger measurements that pull the distribution to the right.

- Center: The center of the distribution can be estimated as the median value, which is the middle measurement when arranged in ascending order. In this case, the median is approximately 5.46.

- Spread: The spread of the distribution can be estimated by looking at the range, which is the difference between the largest and smallest measurements. In this case, the range is approximately 0.97.

- Outliers: Outliers are extreme values that deviate significantly from the rest of the data. From the stemplot, we can see that there are no clear outliers present in the measurements.

(c) To estimate the density of the Earth based on these measurements, we can calculate the mean of the measurements. Summing up all the measurements and dividing by the total number of measurements, we get:

(5.50 + 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 + 5.10 + 5.27 + 5.39 + 5.42 + 5.47 + 5.63 + 5.34 + 5.46 + 5.30 + 5.75 + 5.68 + 5.85) / 29 ≈ 5.46

Based on these measurements, our estimate of the density of the Earth is approximately 5.46 times the density of water.

It's important to note that this estimate is based on the specific measurements taken by Henry Cavendish. Further research and measurements are needed to obtain a more accurate and precise value for the density of the Earth.

Step-by-step explanation: