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)}.
Average Value and Calculation
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.
Table of Content
- What is Average Value?
- Types of Averages
- Arithmetic Mean
- Median
- Mode
- Comparing Mean, Median, and Mode
- Solved Examples on Average Value
- Practice Questions on Average Value