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Class Mark

Class mark, in statistics, is the average of the upper limit and the lower limit of a class in a frequency distribution. In other words, the class mark is the mid-value of the given class interval.

1.	What is Class Mark?
2.	Class Mark Formula
3.	Class Mark in Frequency Distribution
4.	FAQs on Class Mark

What is Class Mark?

Class mark in a frequency distribution is the midpoint or the middle value of a given class. For example, the class mark of 10-20 is 15, as 15 is the mid-value that lies between 10 and 20. In statistics, the class mark is used at various places, for example, while calculating mean, drawing line graphs, finding the average of each class in a frequency distribution, etc. It is very easy to calculate class mark by using a formula that you will learn in the section below.

Class Mark Formula

The formula to calculate class mark in a frequency distribution is given as (upper limit + lower limit)/2 or (Sum of class boundaries)/2. By using this class mark formula, you can easily find the midpoint of any given class interval.

class mark formula

Let us learn the terms associated with this formula in detail.

Class Interval: It is defined as the size of each class of numerical data in a large frequency distribution following a specific width. For example, if the raw data has too many variations in numbers, we make groups of intervals to organize the data such as 0-10, 10-20, 20-30, etc. These are known as class intervals.

Upper Limit: It is the highest value of the class interval. There could be no item greater than the upper limit in that particular class. For example, the upper limit of 30-40 is 40. It is known as the upper-class boundary.

Lower Limit: It is the lowest value of the class interval. There could be no item less than the lower limit in that particular class. For example, the lower limit of 30-40 is 30. It is known as lower class boundary.

Class Mark in Frequency Distribution

In a histogram (a graphical representation of a frequency distribution), we can easily find the midpoint of each class by observing the values at the x-axis or the horizontal axis. By applying the formula of class mark, let us find the values of class marks for each class in the given distribution showing the salaries of employees working in a company.

Salaries (in $)	Number of Employees	Class Mark (in $)
0-10	50	5
10-20	300	15
20-30	260	25
30-40	400	35
40-50	550	45
50-60	450	55

Let us show this information in a histogram and denote the values of class marks through a dotted line in the middle of each bar representing the range of salaries.

class mark in frequency distribution

One interesting fact here is that if we join the mid points on the top of each bar, we can draw a line graph.

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Class Mark Examples

Example 1: What will be the class mark of the given class: 25 - 35?

Solution: By using the class mark formula, we have, Class mark = (upper limit + lower limit)/2. The given class is 25 - 35, where 25 is the lower limit and 35 is the upper limit.

⇒ Class mark = (35 + 25)/2

= 60/2

= 30

Therefore, the class mark of 25 - 35 is 30.
Example 2: If the class mark is given as 55 and the upper limit is 65, find the value of the lower limit of the class interval?

Solution: Given, class mark = 55.

⇒ (upper limit + lower limit)/2 = 55

⇒ 65 + lower limit = 55 × 2

⇒ lower limit = 110 - 65

⇒ lower limit = 45

Therefore, the value of the lower limit is 45, and the class interval is 45 - 65.
Example 3: Find the class marks of the following frequency distribution table:

Class Interval Frequency

0-10 2

10-20 5

20-30 8

30-40 4

40-50 1

Solution: Let us write the class marks of each of the intervals by adding an additional column in the given table.

Class Interval Frequency Class Mark

0-10 2 (0+10)/2 = 5

10-20 5 (10+20)/2 = 15

20-30 8 (20+30)/2 = 25

30-40 4 (30+40)/2 = 35

40-50 1 (40+50)/2 = 45

Class Interval	Frequency
0-10	2
10-20	5
20-30	8
30-40	4
40-50	1

Class Interval	Frequency	Class Mark
0-10	2	(0+10)/2 = 5
10-20	5	(10+20)/2 = 15
20-30	8	(20+30)/2 = 25
30-40	4	(30+40)/2 = 35
40-50	1	(40+50)/2 = 45

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Practice Questions on Class Mark

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FAQs on Class Mark

What is Class Mark in Statistics?

The class mark is also known as the midpoint of the class interval in a frequency distribution. It can be defined as the average of the upper limit and the lower limit of a class.

What is the Formula of Class Mark?

The formula to find class mark is given as, Class mark = (upper limit + lower limit)/2, or (sum of class boundaries)/2. For example, to find the class mark of the interval 25-30, we add these values which give us 25 + 30 = 55. Now we divide it by 2 to find the average. This implies, 55/2 = 27.5. So, 27.5 is the class mark of 25 - 30.

What is the Class Mark of the Class Interval 90-120?

By using the class mark formula, we get, Class mark of 90-120 = (90 + 120)/2 = 210/2 = 105. Therefore, 105 is the class mark of 90 - 120.

What is the Class Mark of a Class a-b?

If a and b are the values of the lower limit and the upper limit respectively, then the class mark is (a + b)/2.

How to Find Class Mark?

We can find the class mark of any given class interval by finding the average of the upper limit and the lower limit. In other words, simply add the values of class boundaries and divide the sum by 2.

What is the Class Mark of Class 100-190?

By using the class mark formula, we get, Class mark of 100-190 = (100 + 190)/2 = 290/2 = 145. Therefore, 145 is the class mark of 100 - 190.

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