Question

The classes are 5-9, 10-14, 15-19, 20-24 .... Find the lower boundary of the class 15-19 and the upper boundary of the class 10-14.​

Answer 1

Final answer:

The lower boundary of class 15-19 = 14.5

The upper boundary of class 10-14 = 14.5

Given that: We are given classes: 5-9, 10-14, 15-19, 20-24

To find: We have to find the lower boundary of the class: 15-19 and the upper boundary of the class: 10-14.​

Explanation:

• Here, the given frequency distribution is grouped but not continuous. So, first, we will make the frequency distribution regular.

Let’s take the first and second class intervals.

• The lower limit of the second class interval of the given frequency distribution = 10
• The upper limit of the first class interval of the given frequency distribution = 9
• The difference between the lower limit of the second class interval and the upper limit of the class interval of given frequency distribution is denoted by "h", here h $= 10 - 9 = 1$

Therefore, $\frac{h}{2} =\frac{1}{2}=0.5$

• To make class intervals, we need to add $0.5$ to the upper limit and reduce $0.5$ from the lower limit of a class boundary of the given frequency distribution.

Class boundaries:

$5-9= 4.5-9.5\\\\10-14 = 9.5-14.5\\\\15-19=14.5-19.5\\\\20-24=19.5-24.5$

• So, the lower boundary of class 15-19 = 14.5

• The upper boundary of class 10-14 = 14.5

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Answer 2

• Lower boundary of the class 15 - 19 is 14.5

• Upper boundary of the class 10 - 14 is 14.5

Given :

The classes are 5 - 9, 10 - 14, 15 - 19, 20 - 24, ....

To find :

• Lower boundary of the class 15 - 19

• Upper boundary of the class 10 - 14

Concept :

Class boundary :

When class intervals are such a type that the upper class limit of any class is not equal to lower class limit of successive class then to get any continuous graphical representation of the data it is sometimes required to rearrange the class limits in such a way that the upper class limit of any class coincides with the lower class limit of next class. Then these class limits are called class boundaries. The lower and upper ends of any class are called lower and upper class boundaries respectively.

Solution :

Step 1 of 3 :

Find the class boundaries

Here the given classes are 5 - 9, 10 - 14, 15 - 19, 20 - 24, ....

So the class boundaries are

4.5 - 9.5 , 9.5 - 14.5 , 14.5 - 19.5 , 19.5 - 24.5 so on

Step 2 of 3 :

Find lower boundary of the class 15 - 19

The class boundaries for the class 15 - 19 is 14.5 - 19.5

Hence lower boundary of the class 15 - 19 is 14.5

Step 3 of 3 :

Find upper boundary of the class 10 - 14

The class boundaries for the class 10 - 14 is 9.5 - 14.5

Hence upper boundary of the class 10 - 14 is 14.5

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