Q.11 - Elementary Statistics

Question

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 $5$ 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 cut-points of the third class?

d. Which class would contain an observation of ?

Step-by-Step Solution

Answer

(a) The most common class width is $10$

(b)  The cut-points average is $20$.

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

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

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.

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 $10$.

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.

Part (b) Step 2: Explanation

The average of the cut-points is the midpoints.

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

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

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.

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 $25$ and $35$.

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.

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 $32.4$ does 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 $32.4$ is in third class.