Examples of Mean Formula

Example 1: Calculate the mean of the first 5 even natural numbers.

Solution: 

Given,

• Observed first 5 even natural numbers 2, 4, 6, 8, 10
• Total number of observed values = 5

Using Mean Formula

Mean = (Sum of observed values in data)/(Total number of observed values in data)

⇒ Sum of observed values = 2 + 4 + 6 + 8 + 10 = 30

Total number of observed values = 5

⇒ Mean = 30/5

⇒ Mean = 6 

Therefore, mean for first 5 even numbers = 6

Example 2: Calculate the mean of the first 10 natural odd numbers.

Solution: 

Given,

• Observed first 5 odd natural numbers 1, 3, 5, 7, 9.
• Total number of observed values = 5

Using Mean Formula

Mean = (Sum of observed values in data)/(Total number of observed values in data)

Sum of observed values = 1 + 3 + 5 + 7 + 9 = 25

Total number of observed values = 5

⇒ Mean = 25 / 5

⇒ Mean = 5

Therefore, mean for first 5 odd numbers = 5

Example 3: Calculate missing values from the observed set 2, 6, 7, x, whose mean is 6.

Solution:

Given,

• Observed values 2, 6, 7, x
• Number of observed values = 4
• Mean = 6

Using Mean Formula

Mean = (Sum of observed values in data)/(Total number of observed values in data)

⇒ Sum of observed values = 2 + 6 + 7 + x = 15 + x

Total number of observed values = 4

⇒ 6 = (15 + x)/4

⇒ 6 × 4 = 15 + x

⇒ x = 9

Therefore, missing value from the set is 9

Example 4: There are 20 students in class 10. The marks obtained by the students in mathematics (out of 100) are given below. Calculate the mean of the marks.

Solution:

Given,

• Total number of students in class 10 = 20
• x₁ = 100, x₂ = 92, x₃ = 80, x₄ = 75, x₅ = 70
• f₁ = 1, f₂ = 3, f₃ = 5, f₄ = 10, f₅ = 1

Using Mean Formula

⇒ x̄ = {(100 × 1) + (92 × 3) + (80 × 5) + (75 × 10) + (70 × 1)}/20

⇒ x̄ = (100 + 276 + 400 + 750 + 70)/20 

⇒ x̄ = 1596/20 = 79.8 marks

Example 5: Calculate the mean of the following dataset.

Solution:

Range of data is 60 to 76, for assumption of mean, lets take average of the range values,

Assumed Mean = (60 + 76) /2 = 136/2 = 68

Now, Let’s A = 68 be assumed mean of the data,

Now, using assumed mean value, let’s create the table for step deviation as follows:

Thus, Mean = 68 + 2 × (-10.5)/25 

⇒ Mean = 68 + 2 × (-0.42) 

⇒ Mean = 68 – 0.84 = 67.16

Thus, mean height of data using step deviation method is 67.16 inches.

Mean in Mathematics is the measure of central tendency and is mostly used in Statistics. Mean is the easiest of all the measures. Data is of two types, Grouped data and ungrouped data. The method of finding the mean is also different depending on the type of data. Mean is generally the average of a given set of numbers or data. It is one of the most important measures of the central tendency of distributed data.

In statistics, the mean is the average of a data set. It is calculated by adding all the numbers in the data set and dividing by the number of values in the set. The mean is also known as the average. It is sensitive to skewed data and extreme values. For example, when the data are skewed, it can miss the mark.

In this article, we’ll explore all the things you need to know about What is Mean, Mean Definition, Mean Formula, Mean Examples, and others in detail.