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Chapter 2: Q. 2.89 (page 70)

Use the specified grouping method to

Part (a): Determine a frequency distribution.

Part (b): Obtain a relative frequency distribution.

Part (c): Construct a frequency histogram based on your result from part (a).

Part (d): Construct a relative frequency histogram based on your result from part (b).

The cheetah is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceed speeds of 60mph and according to the online document "Cheetah Conservation in Southern Africa" by J. Urbaniak, the cheetah is capable of speeds up to 72mph.The following table gives the speeds, in miles per hour, over 14 mile for 35cheetahs. Use cutpoint grouping with 52as the first cutpoint and classes of equal width 2.

Short Answer

Expert verified

Part (a): A frequency distribution is given below,

Part (b): A relative-frequency distribution is given below,

Part (c): On constructing a histogram using part (a), we get,

Part (d): On constructing a relative frequency histogram using part (b), we get,

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given question,

02

Part (a) Step 2. Determine a frequency distribution.

We know that to use cutpoint grouping with a first class of 52as the first cutpoint and classes of equal width 2.

This class is for speeds of 52miles per hour, up to but not including 54miles per hour. The largest value of speedsis 75.3millions per hour, so the last class must be 74-under 76. Therefore, grouping by 2s results 12classes.

The frequency distribution for the speeds of cheetahs using cutpoint grouping is given below,

03

Part (b) Step 1. Determine the relative-frequency distribution.

The formula of the relative frequency is Relativefrequency=FrequencyNumberofobservations.

The relative frequency distribution is given below,

04

Part (c) Step 1. Construct a frequency histogram.

On constructing a histogram using part (a) is given below,

We can see that the given data is approximately symmetric. Also, we can see that there exists one outlier in the data.

05

Part (d) Step 1. Construct a relative frequency histogram.

On constructing a relative frequency histogram using part (b) is given below,

We can see that the given data is approximately symmetric. Also, we can see that there exists one outlier in the data.

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