Average
The average is of two or more similar quantities is the quantity obtained by dividing the sum of the quantities by the number of quantities. Another term is used for Average which is “Arithmetic Means”
The sum of the quantities
Average = ------------------------------------------
The number of the quantities
So, The sum of the quantities = Average X The number of the quantities
There is some important note, in the time of addition of the quantity the unit should be the same but the time of division unit may differ.
Example-
1) The number of student attending a class during a week were Monday- 35, Tuesday-42, Wednesday- 48, Thursday – 37, Friday – 40 and Saturday – 38. Find the average daily attendance.
Ans.) We can see that, according to the daily attendance of student like this –
Monday – 35
Tuesday – 42
Wednesday – 48
Thursday – 37
Friday – 40
Saturday – 38
So, weekly (Monday to Saturday) attendance = (35 + 42 + 48 + 37 + 40 + 38) students
Total days from Monday to Saturday = 6 days
Total student attendance
Average attendance = ---------------------------------
Total number of days
35 + 42 + 48 + 37 + 40 + 38 240
Average attendance = -------------------------- = -------
6 6
= 40 students (Ans.)
2) If 7 books cost $ 30 each and 3 books cost $ 40 each, then find the average cost of the books ?
Ans.) 7 books cost $ 30 each, so total cost of 7 books = 30 X 7 = $ 210
3 books cost $ 40 each, so total cost of 3 books = 40 X 3 = $ 120
Total number of books = 7 + 3 = 10 books
Total costing to purchase all these 10 books = 210 + 120 = $ 330
330
So, the average cost of books are = ---------- = $ 33
10
The average cost of the books is $ 33 (Ans.)
3) The average age of 6 persons is 14.5 years, the average age of 4 of them is 13.25 years. If the age of the fifth person is 16 years find the age of the sixth person.
Ans.) The average age of 6 person is 14.5 years, so the total age of the 6 person is 14.5 X 6 = 87 years
As per the given condition, the average age of 4 of them is 13.25 years, so the total age of the first 4 persons is = 13.25 X 4 = 53 years
If the age of fifth person is 16 years, then the age of sixth person is = Total age of 6 person – (total age of 4 person + age of fifth person)
So, 87 – ( 53 + 16) = 87 – 69 = 18 years
The age of Sixth person is 18 years (Ans.)
4) The average weight of 10 students in a class is 53 kg. when the weight of the teacher is added, the average weight goes up by 2 kg. find the weight of the teacher
Ans.) The average weight of 10 students in a class is 53 kg,
so the total weight of 10 students is = 53 X 10 = 530 kg
if the weight of a teacher has been added then the average weight of students with teacher is increased by 2 kg, hence the average weight of 11 people is 53 + 2 = 55 kg.
So, total weight of 11 people is = 55 X 11 = 605
The weight of the teacher is = total weight of 11 people – total weight of 10 people = 605 – 530 = 75 kg
The weight of the teacher is 75 kg (Ans.)