Solved Examples on Average Value

Problem 1: A teacher recorded the marks of 5 students in a mathematics test. The marks obtained by the students are 85, 90, 75, 80, and 95. Find the average marks scored by the students.

Solution:

To find the average marks, we sum up all the marks and then divide by the total number of students.

Total marks = 85 + 90 + 75 + 80 + 95

= 425

Number of students = 5

Average marks = Total marks / Number of students

= 425 / 5

= 85

So, the average marks scored by the students is 85.

Problem 2: The average age of a group of 6 friends is 25 years. If the ages of 5 friends are 22, 24, 26, 27, and 28 years respectively, what is the age of the sixth friend?

Solution:

Let’s denote the age of the sixth friend as  x.

Given that the average age of 6 friends is 25 years:

Total age of 6 friends = Average age × Number of friends

= 25 × 6

= 150 years

Now, we subtract the total age of 5 known friends from the total age of 6 friends to find the age of the sixth friend:

 x + 22 + 24 + 26 + 27 + 28 = 150

 x + 127 = 150

 x = 150 – 127

 x = 23

So, the age of the sixth friend is 23 years.

Problem 3: We have a set of numbers that is 5, 3, 0, 6, 4, 3, 7, 1, 10, 9, 8. Find the mean, median, and mode.

Solution:

Mean:

5+3+0+6+4+3+7+1+8+9+10 = 56 and 56/10 = 5.6

Median:

5 (after arranging in ascending order 0,1,3,3,4,5,6,7,8,9,10 the middle term is 5)

Mode:

3 {as it is repeated the highest number of times(2 times)}.

Understanding averages is a fundamental aspect of quantitative analysis across various fields, from finance to academia, from sports to business. Whether it’s determining the average income of a population or the average score of a student, the concept of average value serves as a crucial tool for summarizing data and drawing meaningful insights. In this article, we delve into the essence of average value, its significance, and the methods to calculate it.