Q.10 - Elementary Statistics

Question

A quantitative data set has been grouped by using limit grouping with equal-width classes of width 5. The class limits are whole numbers.

a. If the class mark of the first class is 8, what are its lower and upper limits?

b. What is the class mark of the second class?

c. What are the lower and upper limits of the third class?

d. Which class would contain an observation of 28 ?

Step-by-Step Solution

Answer

(a) The first class's top and lower limitations are $10$ and $6$

(b)  The second class's classmark is $13$.

(c) The third class's top and lower limitations are $20$ and $16$

(d) The observation of $28$ is found in the fourth 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 (a) Step 2: Explanation

Limit grouping with equal-width classes was used to group a quantitative data set. 

The width of the class is $5$

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

The average of the limitations is $8$ and the class breadth is $5$.

As a result, the first class's top and lower limitations are $10$ and $6$, respectively.

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

Limit grouping with equal-width classes was used to group a quantitative data set.

The first class has a lower and upper limit of $3$ and $8$, respectively.

The width of the class is six.

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

The second class mark is equal to the first-class mark multiplied by the class width.

As a result, the second class's classmark is $13$.

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

Limit grouping with equal-width classes was used to group a quantitative data set. The width of the class is $5$.

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

The third-grade class mark is determined by

$13+5=18$

As a result, the third class's top and lower limitations are $20$ and $16$, respectively.

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.

Calculation: The observation of $28$ is in fifth class because it is outside of the fourth class's lower and upper bounds.

As a result, the observation of $28$ is found in fourth class.