Q.2.82 - Elementary Statistics

Question

Cottonmouth Litter Size. In the paper "The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range" (Journal of Herpetology, Vol. 29, No. 3, PP. 391-398), C. Blem and L. Blem examined the reproductive characteristics of the eastern cottonmouth, a once widely distributed snake whose numbers have decreased recently due to encroachment by humans. A simple random sample of 24 female cottonmouths in Florida yielded the following data on number of young per litter. Use single-value grouping.

a. determine a frequency distribution.

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result from part (b).

Step-by-Step Solution

Answer

(a) 

$\begin{array}{rrr}\text{ Value }& \text{ Frequency }& \text{ Relative frequency }\\ 1& 1& 0.042\\ 3& 1& 0.042\\ 4& 3& 0.125\\ 5& 7& 0.292\\ 6& 6& 0.25\\ 7& 4& 0.167\\ \text{8 }& 2& 0.083\\ \mathrm{Total}& 24& 1\end{array}$

(b)

$\begin{array}{rrr}\text{ Value }& \text{ Frequency }& \text{ Relative frequency }\\ 1& 1& 0.042\\ 3& 1& 0.042\\ 4& 3& 0.125\\ 5& 7& 0.292\\ 6& 6& 0.25\\ 7& 4& 0.167\\ \text{8 }& 2& 0.083\\ \mathrm{Total}& 24& 1\end{array}$

(c)

(d) 

Part (a)Step 1: Given information

Given in the question that, In the paper "The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range" (Journal of Herpetology, Vol. 29, No. 3, PP. 391-398), C. Blem and L. Blem examined the reproductive characteristics of the eastern cottonmouth, a once widely distributed snake whose numbers have decreased recently due to encroachment by humans. A simple random sample of 24 female cottonmouths in Florida yielded the following data on number of young per litter. Use single-value grouping.

We need to determine a frequency distribution. 

Part(a) Step 2: Explanation

The given data is

The number of values that fall between the class's bounds is the frequency.

The data's frequency distribution is as follows:

$\begin{array}{rrr}\text{ Value }& \text{ Frequency }& \text{ Relative frequency }\\ 1& 1& 0.042\\ 3& 1& 0.042\\ 4& 3& 0.125\\ 5& 7& 0.292\\ 6& 6& 0.25\\ 7& 4& 0.167\\ \text{8 }& 2& 0.083\\ \mathrm{Total}& 24& 1\end{array}$

Part(b) Step 1: Given information

Given in the question that, In the paper "The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range" (Journal of Herpetology, Vol. 29, No. 3, PP. 391-398), C. Blem and L. Blem examined the reproductive characteristics of the eastern cottonmouth, a once widely distributed snake whose numbers have decreased recently due to encroachment by humans. A simple random sample of 24 female cottonmouths in Florida yielded the following data on number of young per litter. Use single-value grouping.

We need to obtain a relative-frequency distribution. 

Part (b) Step 2: Explanation

The given data is

The frequency is divided by the overall frequency to get the relative frequency.

The data's relative frequency distribution is as follows:

$\begin{array}{rrr}\text{ Value }& \text{ Frequency }& \text{ Relative frequency }\\ 1& 1& 0.042\\ 3& 1& 0.042\\ 4& 3& 0.125\\ 5& 7& 0.292\\ 6& 6& 0.25\\ 7& 4& 0.167\\ \text{8 }& 2& 0.083\\ \mathrm{Total}& 24& 1\end{array}$

Part(c) Step 1: Given information

Given in the question that, In the paper "The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range" (Journal of Herpetology, Vol. 29, No. 3, PP. 391-398), C. Blem and L. Blem examined the reproductive characteristics of the eastern cottonmouth, a once widely distributed snake whose numbers have decreased recently due to encroachment by humans. A simple random sample of 24 female cottonmouths in Florida yielded the following data on number of young per litter. Use single-value grouping.

We need to construct a frequency histogram based on the result from part (a) 

Part(c) Step 2: Explanation

The given data is

On a horizontal axis, the histogram shows the quantitative data classes, and on a vertical axis, the frequencies of those classes.

The bars must all be the same width and must be bordered by the lower class limitations.

The frequency must be represented by the height of the bars.

The frequency distribution histogram is shown below:

Part(d) Step 1: Given information

Given in the question that, In the paper "The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range" (Journal of Herpetology, Vol. 29, No. 3, PP. 391-398), C. Blem and L. Blem examined the reproductive characteristics of the eastern cottonmouth, a once widely distributed snake whose numbers have decreased recently due to encroachment by humans. A simple random sample of 24 female cottonmouths in Florida yielded the following data on number of young per litter. Use single-value grouping.

We need to construct a relative-frequency histogram based on the result from part (b) 

Part(d) Step 2: Explanation

The given data is

On a horizontal axis, the histogram shows the quantitative data classes, and on a vertical axis, the frequencies of those classes.

 The bars must be of the same width and must be bordered by the lower class limits.

The frequency must be represented by the height of the bars.

The relative frequency distribution histogram is shown below: