Q.2.89 - Elementary Statistics

Question

The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of $60\mathrm{mph}$ and, according to the online document "Cheetah Conservation in Southern Africa" (Trade \& Environment Database (TED) Case Studies, Vol. 8, No. 2) by J. Urbaniak, the cheetah is capable of speeds up to$72\mathrm{mph}$. The following table gives the speeds, in miles per hour, over $1 / 4$ mile for 35 chectahs. Use cutpoint grouping with 52 as the first cutpoint and classes of equal width 2 .

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)

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 52<54& 2& 0.057\\ 54<56& 5& 0.143\\ 56<58& 6& 0.171\\ 58<60& 8& 229\\ 60<62& 7& 0.2\\ 62<64& 3& 0.086\\ 64<66& 2& 0.057\\ 66<68& 1& 0.029\\ 68<70& 0& 0\\ 70<72& 0& 0\\ 72<74& 0& 0\\ 74<76& 1& 0.029\\ \text{ Total }& 35& 1\\ \hline\end{array}$

(b)

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 52<54& 2& 0.057\\ 54<56& 5& 0.143\\ 56<58& 6& 0.171\\ 58<60& 8& 229\\ 60<62& 7& 0.2\\ 62<64& 3& 0.086\\ 64<66& 2& 0.057\\ 66<68& 1& 0.029\\ 68<70& 0& 0\\ 70<72& 0& 0\\ 72<74& 0& 0\\ 74<76& 1& 0.029\\ \text{ Total }& 35& 1\\ \hline\end{array}$

(c)

(d)

 

Part (a)Step 1: Given information

Given in the question that,  The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of $60\mathrm{mph}$ and, according to the online document "Cheetah Conservation in Southern Africa" (Trade \& Environment Database (TED) Case Studies, Vol. 8, No. 2) by J. Urbaniak, the cheetah is capable of speeds up to $72\mathrm{mph}$. The following table gives the speeds, in miles per hour, over $1 / 4$ mile for 35 chectahs. Use cutpoint grouping with 52 as the first cutpoint and classes of equal width 2 .

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:

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 52<54& 2& 0.057\\ 54<56& 5& 0.143\\ 56<58& 6& 0.171\\ 58<60& 8& 229\\ 60<62& 7& 0.2\\ 62<64& 3& 0.086\\ 64<66& 2& 0.057\\ 66<68& 1& 0.029\\ 68<70& 0& 0\\ 70<72& 0& 0\\ 72<74& 0& 0\\ 74<76& 1& 0.029\\ \text{ Total }& 35& 1\\ \hline\end{array}$

Part(b) Step 1: Given information

Given in the question that,  The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of $60\mathrm{mph}$ and, according to the online document "Cheetah Conservation in Southern Africa" (Trade \& Environment Database (TED) Case Studies, Vol. 8, No. 2) by J. Urbaniak, the cheetah is capable of speeds up to $72\mathrm{mph}$. The following table gives the speeds, in miles per hour, over $1 / 4$ mile for 35 chectahs. Use cutpoint grouping with 52 as the first cutpoint and classes of equal width 2 .

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:

$\begin{array}{|lll|}\hline \text{ Class }& \text{ Frequency }& \begin{array}{l}\text{ Relative }\\ \text{ frequency }\end{array}\\ 52<54& 2& 0.057\\ 54<56& 5& 0.143\\ 56<58& 6& 0.171\\ 58<60& 8& 229\\ 60<62& 7& 0.2\\ 62<64& 3& 0.086\\ 64<66& 2& 0.057\\ 66<68& 1& 0.029\\ 68<70& 0& 0\\ 70<72& 0& 0\\ 72<74& 0& 0\\ 74<76& 1& 0.029\\ \text{ Total }& 35& 1\\ \hline\end{array}$

Part(c) Step 1: Given information

Given in the question that,  The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of $60\mathrm{mph}$ and, according to the online document "Cheetah Conservation in Southern Africa" (Trade \& Environment Database (TED) Case Studies, Vol. 8, No. 2) by J. Urbaniak, the cheetah is capable of speeds up to$72\mathrm{mph}$. The following table gives the speeds, in miles per hour, over $1 / 4$ mile for 35 chectahs. Use cutpoint grouping with 52 as the first cutpoint and classes of equal width 2 .

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,  The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of $60\mathrm{mph}$ and, according to the online document "Cheetah Conservation in Southern Africa" (Trade \& Environment Database (TED) Case Studies, Vol. 8, No. 2) by J. Urbaniak, the cheetah is capable of speeds up to $72\mathrm{mph}$. The following table gives the speeds, in miles per hour, over $1 / 4$ mile for 35 chectahs. Use cutpoint grouping with 52 as the first cutpoint and classes of equal width 2 .

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 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 relative frequency distribution histogram is shown below: