The formula given below can be used to find average of the given values.
Problem 1 :
Chicago can get a lot of rain in the rainy season. The rainfall during a period of 6 days was 90 mm, 74 mm, 112 mm, 30 mm, 100 mm and 44 mm. Find the average daily rainfall during this period.
Solution :
Average daily rainfall :
= 75 mm per day
Problem 2 :
Compare the average of the three even whole numbers from 2 to 6 and the average of the four odd whole numbers from 1 to 7.
Solution :
Three even whole numbers from 2 to 6 :
2, 4, 6
Average of three even whole numbers from 2 to 6 :
= 4 ----(1)
Four odd whole numbers from 1 to 7
1, 3, 5, 7
Average of four odd whole numbers from 1 to 7 :
= 4 ----(2)
Comparing (1) and (2),
4 = 4
Average of the three even whole numbers from 2 to 6 and the average of the four odd whole numbers from 1 to 7 are equal.
Problem 3 :
Chicago can get a lot of rain in the rainy season. The rainfall during a period of 6 days was 90 mm, 74 mm, 112 mm, 30 mm, 100 mm and 44 mm. Find the average daily rainfall during this period.
Solution :
Average daily rainfall :
= 75 mm per day
Problem 4 :
A dog slept 6 hours on Sunday, 8 hours on Monday and 420 minutes on Tuesday. Find the average number of hours the dog slept per day.
Solution :
Sunday ----> 6 hrs
Monday ----> 8 hrs
Tuesday ----> 420 min = ⁴²⁰⁄₆₀ hrs = 7 hrs
Average number of hours the dog slept per day :
= 7
Problem 5 :
Mr. Lenin finds the average of the following numbers.
3, 8, 19, 17, 21, 14, k
If the average found by him is 12, find the value of k.
Solution :
Given : Average of 3, 8, 19, 17, 21, 14 and k is 12.
Multiply both sides by 12.
82 + k = 84
Subtract 82 from both sides.
k = 2
Problem 6 :
Find the average of all prime numbers between 30 and 50.
Solution :
The prime numbers between 30 and 502 are
31, 37, 41, 43, 47
Average of all prime numbers between 30 and 50 :
= 39.8
Problem 7 :
Find the average of first 50 natural numbers.
Solution :
Formula to find the sum of first n natural numbers :
= ⁿ⁽ⁿ ⁺ ¹⁾⁄₂
Substitute 50.
= ⁵⁰⁽⁵⁰ ⁺ ¹⁾⁄₂
= 25(51)
= 1275
Sum of first 50 natural numbers is 1275.
Average of first 50 natural numbers :
= 25.5
Problem 8 :
If the average of four consecutive integers is 12.5, find the integers.
Solution :
Let x be the first integer.
Then the four consecutive integers are
x, (x + 1), (x + 2), (x + 3)
Given : Average of four consecutive integers is 12.5.
Average = 12.5
Multiply both sides by 2.
2x + 3 = 25
Subtract 3 from both sides.
2x = 22
Divide both sides by 2.
x = 11
x + 1 = 12
x + 2 = 13
x + 3 = 14
Therefore, the four consecutive integers are
11, 12, 13, 14
Problem 9 :
If the average of four consecutive odd integers is 10, find the largest of these integers.
Solution :
Let x be the first odd integer.
Then the four consecutive odd integers are
x, (x + 2), (x + 4), (x + 6)
Given : Average of four consecutive odd integers is 10.
Average = 10
x + 3 = 10
Subtract 3 from both sides.
x = 7
The largest integer :
= x + 6
= 7 + 6
= 13
Problem 10 :
John played 4 games of badminton and scored an average of 12 points per game. The average score of the first 3 games was 10 points per game. Find the points scored by John in the 4th game.
Solution :
Average of 4 games = 12
sum of the points in 4 games = 48 ----(1)
Average of first 3 games = 10
sum of the points in first 3 games = 30 ----(1)
Points scored by John in the 4th game :
= (2) - (1)
= 48 - 30
= 18
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