Weighted Averages

Concepts Examples

When we have to calculate the average of some groups of different things, having different number of elements is being calculated, then it is called the weighted average.

If the number of elements in n different groups be N₁,N₂,N₃ .. N_n and their respective averages be A₁,A₂,A₃...A_n ,

then Weighted average = $\frac{\mathbb{N}_1\cdot A_1+\mathbb{N}_2\cdot A_2+\mathbb{N}_3\cdot A_3...\mathbb{N}_n\cdot A_n}{\mathbb{N}_1+\mathbb{N}_2+\mathbb{N}_3...\mathbb{N}_n}$N₁·A₁+N₂·A₂+N₃·A₃...N_n·A_nN₁+N₂+N₃...N_n 

Question 1 Average cost of buying 5 quality A crackers is 60 and cost of buying 10 quality B crackers is 80. WHhat will be average cost of buying all the crackers.

71.33	72.33
73.33	74.33

C

Total number of employees = 5 + 10 = 15

Average cost of all the crackers = $\frac{5\cdot60+10\cdot80}{5+10}=\frac{300+800}{15}=\frac{1100}{15}=73.33$5·60+10·805+10 =300+80015 =110015 =73.33

Question 2 Average weight of a class of 40 students is 30 and average weight of a class of 20 students is 15. Find the average weight of both the classes combined.

21	22
24	25

D

Average weight = $\frac{40\times30+20\times15}{40+20}=25$40×30+20×1540+20 =25

Question 3 There are two sections A and B of a class, consisting of 36 and 44 students' respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class.

37.25	74.5
36.25	36

A

Total weight of (36+44) Students = (36×40 + 44×35) kg = 2980 kg

Therefore average weight of the whole class = $\frac{2980}{80}$298080  kg

Therefore average weight = 37.25 kg

Question 4 Average salary of 12 employees in company A is 15000 pm and 15 employees is company B is 16000 pm. What will be the average salary of all the employees.

17000	16888
15000	14888

B

Total number of employees = 15 + 12 = 27

Average salary = $\frac{12\cdot18000+15\cdot16000}{12+15}$12·18000+15·1600012+15 

= $\frac{456000}{27}=16888.88$45600027 =16888.88