UAG 1/3 WS Name: Understanding Average Seriously Addictive Maths Time: AVERAGE:

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1 Time: AVERAGE: - is the total amount divided by the number of items in a group. - is the arithmetical mean of a set of given data Average = sum of all the items number of items Notes: *Average is the estimate of what each person/persons have. It is NOT the actual number of items. *We cannot find the individual value of the items if we are only given the average and the number of items. *The average always lies between the smallest and largest numbers in the given group Copyright. All Rights Reserved. Page 1

2 Time: Example: Ann has 5 marbles, Beth has 7 marbles and Caryn has 6 marbles. If all the marbles are shared equally among the 3 girls, how many marbles would each girl get? Before sharing: Ann: Beth: Caryn: Step 1: Find the total number of marbles: = 18 Copyright. All Rights Reserved. Page 2

3 Time: Step 2: Divide the total number of marbles by the number of children. After sharing: 18 3 = 6 Ann: Beth: Caryn: Answer: The average number of marbles each girl has is 6. Copyright. All Rights Reserved. Page 3

4 Time: Try this! Mary, Jo and Tom weigh 18kg, 24kg and 27kg respectively. (a) What is their total mass? (b) What is their average mass? Solution: (a) Total mass of the children = (b) Average mass of 1 child = Total mass of the children Number of children = = 23 kg = 69 kg Copyright. All Rights Reserved. Page 4

5 Time: Practice questions: 1. Find the average of: (a) 35, 29, 42, 58 ( ) 4 = = 41 (b) 1.3, 3.7, 4.5, 3.9 and 7.1 ( ) 5 = = Dora has 20 dolls, Evelyn has 30 dolls, Fay has 45 dolls, Gina has 25 dolls and Helen has 15 dolls. What is the average number of dolls each girl has? Total Number of Dolls = = 135 Average Number of Dolls = = 27 The average number of dolls each girl has is 27. Copyright. All Rights Reserved. Page 5

6 Time: 3. Mr Ong made an average of 40 chairs each day. What is the total number of chairs he made in 5 days? Day 1 Day 2 Day 3 Day 4 Day Total Number of Chairs = 5 x 40 = 200 The total number of chairs Mr. Ong made is John bought a total of 552ml of orange juice. He poured the juice into 6 cups. What is the average volume of juice in each cup? Average volume of Juice = 552 ml 6 = 92 ml The average volume of juice in each cup is 92 ml. Copyright. All Rights Reserved. Page 6

7 Time: m x 3 = 5.13m The height of the man is 1.71m. The estimated height of the tree is 5.13 m. 6a) Raihan took 1h 40 min to complete 25 Math questions. Find the average time taken for each question. (Give your answer in minutes.) 1 h 40 min = min = 100 min Average time for each question = 100 min 25 = 4 min Copyright. All Rights Reserved. Page 7

8 Time: 6b) Ms Ang can make 30 cups of fruit juice in 5 minutes. What is the average number of cups of juice she can make in 1 minute? 5 min = 30 cups 1 min = 30 5 = 6 cups (c) The average mass of 6 men is 72.5 kg. If the mass of 2 more men are 85 kg and 62.2 kg, what is the average mass of the 8 men? Total mass of 8 men = (72.5 x 6) = kg Average mass = kg 8 = kg 72.8 kg Copyright. All Rights Reserved. Page 8

9 Time: 7. The table shows the number of chicken pies sold by Mrs Lee, Mrs Ng and Mrs Tan. Mrs Lee 120 Mrs Ng 265 Mrs Tan 215 What is the average number of chicken pies each lady sold? Total no of pies sold = = 600 pies Average no of pies each lady sold = = 200 pies Copyright. All Rights Reserved. Page 9

10 Time: 8. The table below shows the marks obtained by Steve, Tim and Ron in an English test. Their average mark was 73. (a) What was their total mark? (b) How many marks did Ron obtain? Steve 98 Tim 59 Ron? (a) Total no of marks = 73 x 3 = 219 marks (b) No of marks Ron obtained = = 62 marks Copyright. All Rights Reserved. Page 10

11 Time: 9. The table below shows the time taken by each boy to run 100m. BOY TIME (in seconds) David 10.1 Edward 12 Farhan 11.7 Gaurav 9.4 Hong Yuan? The total time taken by the 5 boys is 54.5 sec. (a) Find the time taken by Hong Yuan ( ) = (b) Find their average time. = 11.3 sec Average time = = 10.9 sec (c) Who was the fastest runner? Gaurav Copyright. All Rights Reserved. Page 11

12 Time: 10. The average height of Irene, Jane, Kelly and May is 135 cm. The total height of Irene, Jane and Kelly is 401 cm. Find the height of May. (Give your answer in metres and centimetres.) Total height of the 4 girls = 135 cm x 4 = 540 cm Height of May = 540 cm 401 cm = 139 cm = 1m 39 cm 11. The average speed of Car A, Car B and Car C is 70 km/h. Car A and Car C have an average speed of 67 km/h. What is the speed of Car B? Total speed = 70 km x 3 = 210 km Speed of Car B = 210 (67 x 2) = 76 km/h Copyright. All Rights Reserved. Page 12

13 Time: 12. The average weight of 9 books is 320 g. 3 of the books weigh 840 g in total. (a) What is the total weight of the other 6 books? (b) What is the average weight of the other 6 books? a) Total weight of 9 books = 320 g x 9 = 2880 g Total weight of the other 6 books = 2880 g 840 g = 2040 g b) Average weight of the other 6 books = 2040 g 6 = 340 g Copyright. All Rights Reserved. Page 13

14 Time: 13. Pen - $2.10 pencil - $1.10 Eraser - $0.80 ruler - $1.40 Ravi bought 2 erasers, 3 pencils, 1 pen and 1 ruler. What is the average cost of the items purchased? Total cost = 2 x $ x $ $ $1.40 = $8.40 Average cost = $ = $1.20 Copyright. All Rights Reserved. Page 14

15 Time: 14. Dress 1 for $63.50 Jeans 2 pairs for $59 T-shirt 2 for $29 Mei Ling bought 2 dresses, 2 pairs of jeans and 4 T- shirts. (a) Find the total cost of the clothes she bought. (b) Find the average cost of the clothes she bought. (a) Total cost = 2 x $ $ x $29 = $244 (b) Average cost = $244 8 = $30.50 Copyright. All Rights Reserved. Page 15

16 Time: 15. Mrs Lim gave her 3 children $100 each. The table shows the amount of money her 3 children spent. NAME AMOUNT SPENT Mark $58 Matthew? Mary $37 The average expenditure of the 3 children was $47. (a) How much did Matthew spend? (b) How much money did the children have left altogether? Copyright. All Rights Reserved. Page 16

17 Time: a) Total expenditure = $47 x 3 = $141 Amount Matthew spent = $141 - $58 - $37 = $46 b) Total amount of money the children have = $100 x 3 = $300 Remainder = $300 - $141 = $159 Copyright. All Rights Reserved. Page 17

18 Time: 16. The average of X and Y is 86. X is 24 more than Y. Find the values of X and Y. X + Y = 172 Y = (172 24) 2 = 74 X = = Mei Ling had 110 stickers. Nancy had 18 fewer stickers than Mei Ling. Olivia had 15 more stickers than Mei Ling. What is the average number of stickers each girl has? Nancy = = 92 Olivia = = 125 Total = = 327 Average number of stickers each girl has = = 109 Copyright. All Rights Reserved. Page 18

19 Time: 18. Tom, Tim, Tony and Titus had an average of 59 toy trains. Tom had 48 trains. The total number of trains that Tim and Tony had was 62 more than the number of trains Titus had. How many trains did Titus have? Total no of trains = 59 x 4 = 236 No of trains Tim, Tony, and Titus have = = 188 No of trains Titus have = (188 62) 2 = 63 toy trains Copyright. All Rights Reserved. Page 19

20 Time: 19. Megan, Nancy, Olivia and Pat had an average of 62 pencils. Megan had 45 pencils. The total number of pencils Nancy and Pat had was 45 more than the number of pencils Olivia had. How many pencils does Olivia have? Total no of pencils = 62 x 4 = 248 No of pencils Nancy, Olivia and Pat have = = 203 No of pencils Olivia has = (203 45) 2 =158 2 = 79 Copyright. All Rights Reserved. Page 20

21 Time: 20. The average of 2 numbers is 280. The first number is 300% the value of the second number. Find the difference between the 2 numbers. Sum of 2 numbers = 280 x 2 = % = % = = % = 140 x 3 = 420 Difference = = 280 Copyright. All Rights Reserved. Page 21

22 Time: 21. A Thomas and friends train set costs $49. A remote control car costs 70% of the Thomas and friends train set. A board game costs half as much as the remote control car. Find the average cost of the 3 items. (Give your answer to the nearest dollar.) Remote control car = (70 100)% x $49 =$34.30 Board game= $ = $17.15 Total cost = $49 + $ $17.15 = $ Average cost = $ =$ $33 Copyright. All Rights Reserved. Page 22

23 Time: 22. Sue used 5 pages of an album to arrange her photos. Each page had 1 more photo than the previous page. The average number of photos in the 5 pages was 5. How many photos are there on the third page? Let the no of photos in the 1 st page be X. 1 st page + 2 nd page + 3 rd page + 4 th page + 5 th page = 5 x 5 = 25 X + (X + 1) + (X + 2) + (X +3) + (X + 4) = 25 5 X + 10 = 25 5 X = 15 X = 3 No of photos in 3 rd page = = 5 photos Copyright. All Rights Reserved. Page 23

24 Time: 23. There are 6 P5 classes. Each class has 1 more pupil than the previous class. The average number of pupils in each class is 37.5 Fill in the table below. CLASS NUMBER OF PUPILS 5A 35 5B 36 5C 37 5D 38 5E 39 5F 40 Let the no of pupils in the 1 st class be X. 1 st class + 2 nd class + 3 rd class + 4 th class + 5 th class + 6 th class = 37.5 x 6 = 225 X + (X + 1) + (X + 2) + (X +3) + (X + 4) + (X + 5) = X + 15 = X = 210 X = 35 Copyright. All Rights Reserved. Page 24

25 Time: 24. The average of 5 numbers is X. When one of the numbers is increased by 128, the average becomes Y. Tick the statements that are true. (Show your working below) The actual value of Y can be found. The difference between X and Y is 25.6 The total value of the 5 numbers cannot be found = 25.6 Copyright. All Rights Reserved. Page 25

26 Time: 25. Mrs Ong wrote down 4 different numbers. They are all greater than 70. The average of the 4 numbers is of the numbers are 78 and 81. What could the 2 remaining numbers be? (Write down 1 possible set of answer.) Total = 82 x 4 = 328 Sum of 2 numbers = 159 Possible remaining numbers = 71 and 98 / 72 and 97 (Accept as long as they both add up to 169 and both numbers are more than 70) Copyright. All Rights Reserved. Page 26

27 Time: 26. The ages of Bill and Joe were 4 yr 1 mth and 5 yr 7 mth respectively. When John joined the group, the average age of the 3 boys was increased by 18 months. Find John s age. (Give your answer in years and months) Total ages of Bill and Joe = 4 yr 1 mth + 5 yr 7 mth = 9 yr 8 mth Average age of Bill and Joe = (9 yr 8 mth) / 2 Average age of Bill, Joe and John = 4yr 10 mth = 4 yr 10 mth + 18 mth = 6 yr 4 mth Total age of Bill, Joe and John = 6 yr 4 mth x 3 = 19 yr John s age = 19 yr 9 yr 8 mth = 9 yr 4 mth Copyright. All Rights Reserved. Page 27