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A quantitative data set has been grouped by using cut-point grouping with equal-width classes of width 8.

a. If the midpoint of the first class is 10, what are its lower and upper cut-points?

b. What is the class 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 22?

Short Answer

Expert verified

(a) The lower and upper cut-points are respectively 6and 14.

(b) The midpoint is18.

(c) The lower and upper cut-points are therefore 22and 33

(d) The observation of 22 is included in the 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 (a) Step 2: Explanation

Cut-point grouping with equal width class of width 8was used to organise a quantitative data set.

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

The lower cut-point is the midpoint that has been reduced by half of the class width, whereas the upper cut-point is the midpoint that has been increased by half of the class width.

As a result, the lower and upper cut-points are respectively 6and 14.

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 middle.

The former midway is increased by class width to create the new midpoint.

As a result, the midpoint is 18.

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 the previous class's upper cut-point, whereas the upper cut-point is the lower cut-point multiplied by the class width.

The lower and upper cut-points are therefore 22and 30, respectively.

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 22is the lowest cut-point of the third class, it contains the observation of 22.

As a result, the observation of 22is included in the third class.

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