Simple Averages

Concepts Examples

Properties of Averages

1. Average of N things/quantities is equal to the sum of all the things/quantities divided by number of things/quantities.

2. Average of N number of things/quantities always lies between the lowest and the highest quantities.

3. If each quantity is increased by a certain value K, then the new average is increased by K.

4. If each quantity is decreased by a certain value K, then the new average is decreased by K.

5. If each quantity is multiplied by a certain value K, then the new average becomes K times the the original average.

6. If each quantity is divided by a certain value K, then the new average becomes $\frac{1}{K}$1K  times the the original average.

Question 1 Average number of chocolates with 10 children is 5. If a person distributes all 20 chocolates he has to the children then what is the average number of chocolates with the children.

7	8
9	10

A

Total number of chocolates with the students = 10 × 5 = 50

New Total number of chocolates = 50 + 20 = 70

∴ new average number of chocolates = $\frac{70}{10}=7$7010 =7

Question 2 The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, then find the average for the last four matches.

35	36
35.25	36.25

C

Total sum of last 4 matches = (10 × 38.9) - (6 × 42)

= 389 - 252 = 137

Average = $\frac{137}{4}=35.25$1374 =35.25

Question 3 Average of a class of 50 students is 50 kg. If 2 guys of average weight 45 leaves the class. What is the new average of the class.

50	50.21
51.2	55.2

B

Total weight of the class = 50 × 50 =2500 kg

Total weight of the two students who leave the class = 45 × 2 = 90 kg

∴new average weight of the class = $\frac{2500-900}{48}=50.21$2500-90048 =50.21

Question 4 The number of sweets in a box is 15. If the shop keeper $\frac{2}{3}$23 ^rd's the number of sweets in each box, then what will be the new average of number of sweets in the box.

5	15
98	10

D

Its simple application of the rule, Since the number of sweets is $\frac{2}{3}$23  of the original quantity in each box

∴ the average number of sweets in each box will be 15 × $\frac{2}{3}$23  = 10

Question 5 If the average weight of a family of 5 people is 42 kg and one member gets married and add to the family. Weight of this member is 48 kg. What will be the new average weight of the family.

42	43
44	45

B

Total weight of the family of 5 people = 5 × 42 = 240

Total weight of family after new member joins the family = 210 + 48 = 258

∴ new average of the family = $\frac{258}{6}=43$2586 =43

Question 6 The number of sweets in a box is 15. If the shop keeper triples the number of sweets in each box, then what will be the new average of number of sweets in the box.

3	15
45	55

C

Its simple application of the rule, Since the number of sweets is tripled in each box

∴ the average number of sweets in each box will be 15 × 3 = 45