Data and charts · Ages 11–12

How a mean changes worksheet

Part of: Line graphs, the mean (average) and pie charts

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Data and charts · Ages 11–12

Numsprite
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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The mean of 6 numbers is 27. With one more number, 41, what is the mean of the 7 numbers?
Answer:
2.The mean of 5 numbers is 39. Subtracting one of them, 67, what is the mean of the 4 left?
Answer:
3.The mean of 5 numbers is 29. Subtracting one of them, 25, what is the mean of the 4 left?
Answer:
4.The mean of 5 numbers is 24. With one more number, 60, what is the mean of the 6 numbers?
Answer:
5.The mean of 6 numbers is 25. After one more number is added, the mean is 32. What number was added?
Answer:
6.The mean of 3 numbers is 32. After one more number is added, the mean is 36. What number was added?
Answer:
7.The mean of 6 numbers is 18. If 7 is added to every number, what is the new mean?
Answer:
8.The mean of 4 numbers is 46. If 10 is added to every number, what is the new mean?
Answer:

9.The mean of 6 numbers is 40. If 58 is added, what happens to the mean?
- A. It goes up
- B. It goes down
- C. Can't tell without the numbers
- D. It stays the same
Choose the right answer
Answer:
10.The mean of 4 numbers is 35. If 40 is added, what happens to the mean?
- A. Can't tell without the numbers
- B. It goes up
- C. It stays the same
- D. It goes down
Choose the right answer
Answer:
11.The mean of 5 numbers is 60. With 56 added, the mean is still 60.
True or false?
Answer:
12.The mean of 5 numbers is 32. With 32 added, the mean is still 32.
True or false?
Answer:

13.Tsz-ching has played 5 games, scoring 79 a game on average. What must the next game score to lift the average to 81?
Working:
Answer:
14.Ming has played 7 games, scoring 61 points a game on average. The next game scores 21. What is the average now?
Working:
Answer:
15.A basketball team of 5 has a mean height of 153 cm. A 149 cm player leaves. What is the mean height of the rest, in cm?
Working:
Answer:
16.A club of 11 has a mean weight of 30 kg. When a new member joins, the mean rises by 2 kg. How heavy is the new member, in kg?
Working:
Answer:
17.A club of 10 has a mean weight of 45 kg. When a new member joins, the mean rises by 2 kg. How heavy is the new member, in kg?
Working:
Answer:
18.Ka-yee has played 3 games, scoring 60 a game on average. What must the next game score to lift the average to 62?
Working:
Answer:

Show the answers and working

How a mean changes worksheet: Answers and working

1. 29
Means can't just be added. Find the old total first: 27 × 6.
Total 27 × 6 = 162; 162 + 41 = 203; 203 ÷ 7 = 29.
2. 32
Find the old total first, 39 × 5, then take 67 away.
Total 39 × 5 = 195; 195 − 67 = 128; 128 ÷ 4 = 32.
3. 30
Find the old total first, 29 × 5, then take 25 away.
Total 29 × 5 = 145; 145 − 25 = 120; 120 ÷ 4 = 30.
4. 30
Means can't just be added. Find the old total first: 24 × 5.
Total 24 × 5 = 120; 120 + 60 = 180; 180 ÷ 6 = 30.
5. 74
Compare two totals: the old total of 6 numbers and the new total of 7.
The total was 150; now 7 numbers total 32 × 7 = 224; 224 − 150 = 74.
6. 48
Compare two totals: the old total of 3 numbers and the new total of 4.
The total was 96; now 4 numbers total 36 × 4 = 144; 144 − 96 = 48.
7. 25
With 7 added to every number, how much does the total grow? Divided by 6, how much does the mean grow?
The total grows by 7 × 6; divided by 6, the mean grows by 7: 18 + 7 = 25.
8. 56
With 10 added to every number, how much does the total grow? Divided by 4, how much does the mean grow?
The total grows by 10 × 4; divided by 4, the mean grows by 10: 46 + 10 = 56.

9. A. It goes up
Compare 58 with the mean, 40: is it bigger, smaller or the same?
A number above the mean raises it, below lowers it, equal leaves it.
10. B. It goes up
Compare 40 with the mean, 35: is it bigger, smaller or the same?
A number above the mean raises it, below lowers it, equal leaves it.
11. False
Which number can be added without changing the mean? Then compare 56 with 60.
The mean stays only if the number added equals it.
12. True
Which number can be added without changing the mean? Then compare 32 with 32.
The mean stays only if the number added equals it.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 91 points
Compare two totals: how many points do 6 games at 81 need, and how many are in already?
6 games need 81 × 6 points; 79 × 5 are in, 91 short.
14. 56 points
Find the total for 7 games first, 61 × 7, then add the new game.
61 × 7 + 21 is the total for 8 games; ÷ 8: 56.
15. 154 cm
Find the team's total height first, 153 × 5, then subtract the player who left.
Total 153 × 5, less 149, ÷ 4: 154.
16. 54 kg
The new mean is 30 + 2. Compare the old and new totals: 11 people and 12.
Now 12 people average 32 kg, total 32 × 12; before, 30 × 11; 54 apart.
17. 67 kg
The new mean is 45 + 2. Compare the old and new totals: 10 people and 11.
Now 11 people average 47 kg, total 47 × 11; before, 45 × 10; 67 apart.
18. 68 points
Compare two totals: how many points do 4 games at 62 need, and how many are in already?
4 games need 62 × 4 points; 60 × 3 are in, 68 short.

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