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

a. If the lower and upper cut-points of the first class are 5and 15, respectively, what is the common class width?

b. What is the midpoint of the second class?

c. What are the lower and upper cut-points of the third class?

d. Which class would contain an observation of ?

Short Answer

Expert verified

(a) The most common class width is 10

(b) The cut-points average is 20.

(c) The lower and upper cut-points are respectively 25and 35.

(d) The observation of 32.4is in third class.

Step by step solution

01

Part (a) Step 1: Concept introduction

A grouping system is a type comprising a correlated activity that integrates any number of members of the subset to generate a factor of the range, with a self - concept and an exact opposite for each component.

02

Part (b) Step 2: Explanation

Cut-point grouping with equal width classes was used to organise a quantitative data set.

The difference between the higher and lower cut-points is the common class width.

As a result, the most common class width is 10.

03

Part (b) Step 1: Concept introduction

A grouping system is a type comprising a correlated activity that integrates any number of members of the subset to generate a factor of the range, with a self - concept and an exact opposite for each component.

04

Part (b) Step 2: Explanation

The average of the cut-points is the midpoints.

The second class's lower and upper cut-points are 15and 25, respectively. The average of the cut-points is the midpoints.

As a result, the cut-points average is 20.

05

Part (c) Step 1: Concept introduction

A grouping system is a type comprising a correlated activity that integrates any number of members of the subset to generate a factor of the range, with a self - concept and an exact opposite for each component.

06

Part (c) Step 2: Explanation

The average of the lower and upper bounds is the class mark.

The lower cut-point is equal to the previous class's upper cut-point, and the upper cut-point is equal to the lower cut-point multiplied by the class width.

As a result, the lower and upper cut-points are respectively 25and 35.

07

Part (d) Step 1: Concept introduction

A grouping system is a type comprising a correlated activity that integrates any number of members of the subset to generate a factor of the range, with a self - concept and an exact opposite for each component.

08

Part (d) Step 2: Explanation

A class's lower class limit is the smallest data value that can be stored in the class.

Because the observation of 32.4does not fall between the lower and upper bounds of the second class, it is placed in the third class.

As a result, the observation of 32.4is in third class.

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