Q. 9 - Elementary Statistics

Question

A quantitative data set has been grouped by using limit grouping with equal-width classes. The lower and upper limits of the first class are $3$ and $8$, respectively, and the class width is $6$.

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

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

c. Which class would contain an observation of $23$ ?

Step-by-Step Solution

Answer

(a) The class mark of the second class is $11.5.$

(b)  The upper and the lower limits of the third class are $20 and 15.$

(c) The fourth class contains the observation of  $23.$

Part (a) Step 1: Given information

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

The lower and upper limits of the first class are $3$ and $8$ .

The class width is $6$ .

Part (a) Step 2: Explanation

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

Calculation: The lower limit for second class is $9$ and the top limit is $14.$

The second class will have a class size of

$=\frac{9+14}{2}$

$=11.5$

Part (b) Step 1: Given Information

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

The lower and upper limits of the first class are $3$ and $8$.

The class width is 6.

Part (b) Step 2: Explanation

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

The lower limit is one higher than the second class's upper limit, and the upper limit is the preceding class's upper limit multiplied by the class width.

Part (c) Step 1: Given Information

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

The lower and upper limits of the first class are $3$ and $8$ respectively.

The class width is $6$.

Part (c) 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 $23$ does not fall within the third class's bottom and higher bounds, it is placed in the fourth class.