A quantitative data set has been grouped by using cutpoint grouping with equal-width classes.

a) If the lower and upper cutpoints of the first class are 5 and 15, respectively, what is the common class width?

b) What is the midpoint of the second class?

c) What are the lower and upper cutpoints of the third class?
d)Which class would contain an observation of $32.4$?

given,

A quantitative data set has been grouped by using cutpoint grouping with equal-width classes.

a) If the lower and upper cutpoints of the first class $5and15$, we find the width of the standard class is shown below:

The minimum limit for the first class is 5.

The maximum limit for the first phase is 15.

$$\begin{gathered} Classwidth=Upperlimit-Lowerlimit \\ =15-5=10 \end{gathered}$$

Therefore, the class width is 10.

The lower cutpoint for the first class is $5$.

The upper cutpoint for the first class is $15$.

In Cutpoint integration the lower cut area of the second phase is equal to the uppercut area of the first phase.

So the Lower cutpoint of the second phase is$15$

The more cutting point of the second phase is,

$$\begin{gathered} =Lowercutpointoftheseconclass+Classwidth \\ =15+10=25 \end{gathered}$$

By definition, the midpoint is given by,

$$\begin{gathered} Midpoint=\frac{Lowercutpoint+Uppercutpoint}{2} \\ =\frac{15+25}{2}=20 \end{gathered}$$

Therefore, the midpoint of the second class is $20$.

The Lower cutpoint of the second class is $15$.

The upper cutpoint for the second phase is $25$.

In Cutpoint collection the lower cut area of the third phase is equal to the uppercut area of the second phase.

So the minimum point for the third stage is$25$

The top cutpoint for the third stage is,

$$\begin{gathered} =Lowerlimitofthethirdclass+Classwidth \\ =25+10=35 \end{gathered}$$

Thus, the lower and upper cutpoints of the third class are$25and35$.

The third class cutpoints are $25and35$
Thus, the third class cutpoints include observation 32.4.