Question

We have presented some quantitative data sets and specified a grouping method for practicing the concepts.

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).

Use cutpoint grouping with a first cutpoint of 25and a class width of 3.

Short answer

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

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

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

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

Step-by-step solution

Part (a) Step 1. Given information.

Consider the given question,

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

Consider the given question,

The first cutpoint is 25and the width of the class interval is 2. Thus, the first class interval is 2.

Then, the first class interval is 25-under 28.

The second class is 28-under 31.Also, the highest observation is 43.01.

Therefore, the last class is 43-under 46.

The frequency distribution using limit grouping is given below,

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

The formula of the relative frequency is $Relativefrequency=\frac{Frequency}{Numberofobservations}$.

Thus, the relative frequency distribution is given below,

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

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

Here, it is clear that the height of the bar represents the frequency obtained in part (a).

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

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

Here, it is clear that the height of the bar represents the relative-frequency obtained in part (b).