Data and probability · Ages 14–15

How changing the data changes the averages worksheet

Part of: Measures of central tendency

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Data and probability · Ages 14–15

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

1.15 items have a mean price of $264. Every price goes up by $10. What is the new mean price, in dollars?
Answer:
2.14 ropes have a median length of 24 m. If each is swapped for one 4 times as long, what is the new median, in m?
Answer:
3.13 items have a mean price of $198.5. Every price goes up by $20. What is the new mean price, in dollars?
Answer:
4.21 ropes have a median length of 33.5 m. If each is swapped for one 2 times as long, what is the new median, in m?
Answer:
5.A team's 4 players have a mean weight of 52 kg. A new player of 69 kg joins. What is the mean weight of the 5, in kg?
Answer:
6.A team's 9 players have a mean weight of 23 kg. A new player of 61 kg joins. What is the mean weight of the 10, in kg?
Answer:
7.19 data have a mean of 16. Each value has 9 added, then is multiplied by 2. What is the new mean?
Answer:
8.33 data have a mean of 32. Each value has 5 added, then is multiplied by 3. What is the new mean?
Answer:

9.8 data have a mean of 54. The value 46 is put in. What happens to the mean?
- A. It can't be told
- B. It falls
- C. It rises
- D. It stays the same
Choose the right answer
Answer:
10.7 data have a mean of 44. The value 44 is put in. What happens to the mean?
- A. It can't be told
- B. It rises
- C. It stays the same
- D. It falls
Choose the right answer
Answer:
11.21 data have a median of 51. Each value is multiplied by 3, then has 3 taken away. The new median is 150.
True or false?
Answer:
12.19 data have a median of 24. Each value is multiplied by 2, then has 9 taken away. The new median is 39.
True or false?
Answer:

13.A city's highest temperatures over 9 days average 28°C. Each day's is changed to Fahrenheit (°F = 1.8 × °C + 32). What is the mean in °F?
Working:
Answer:
14.An archery squad's 20 members average 56 points in a round. Then it turns out one score of 53 was recorded as 33. What is the correct mean?
Working:
Answer:
15.A firm's 24 staff have a mean monthly pay of $25,000 and a median of $18,900. Next year everyone gets a $1,200 rise. The new mean is dollars and the new median dollars.
Fill in each blank
Working:
Answer:
16.A choir's 5 singers have a mean age of 69. A new singer aged 69 joins, and the mean age of the 6 is still 69.
True or false?
Working:
Answer:
17.A choir's 10 singers have a mean age of 70. A new singer aged 67 joins, and the mean age of the 11 is still 70.
True or false?
Working:
Answer:
18.A city's highest temperatures over 19 days average 25°C. Each day's is changed to Fahrenheit (°F = 1.8 × °C + 32). What is the mean in °F?
Working:
Answer:

Show the answers and working

How changing the data changes the averages worksheet: Answers and working

1. 274 dollars
Add the same amount to every value and the mean goes up by it: 264 + 10 = 274.
2. 96 m
Multiply every value by the same number and the order stays, so the median is multiplied too: 24 × 4 = 96.
3. 218.5 dollars
Add the same amount to every value and the mean goes up by it: 198.5 + 20 = 218.5.
4. 67 m
Multiply every value by the same number and the order stays, so the median is multiplied too: 33.5 × 2 = 67.
5. 55.4 kg
The old total is 4 × 52 = 208; with the new player 208 + 69 = 277; over 5: 55.4 kg.
6. 26.8 kg
The old total is 9 × 23 = 207; with the new player 207 + 61 = 268; over 10: 26.8 kg.
7. 50
In order: adding 9 makes the mean 16 + 9 = 25; times 2: 25 × 2 = 50.
8. 111
In order: adding 5 makes the mean 32 + 5 = 37; times 3: 37 × 3 = 111.

9. B. It falls
Compare 46 with the old mean 54: above it, the mean rises; below, it falls; equal, it stays.
10. C. It stays the same
Compare 44 with the old mean 44: above it, the mean rises; below, it falls; equal, it stays.
11. True
Multiply, then subtract: 51 × 3 − 3 = 150 (subtracting first would give 144).
12. True
Multiply, then subtract: 24 × 2 − 9 = 39 (subtracting first would give 30).

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

13. 82.4°F
Every value is multiplied by 1.8 and has 32 added, so the mean too: 1.8 × 28 + 32 = 82.4.
14. 57 points
The recorded total is 20 × 56 = 1120; corrected, 1120 − 33 + 53 = 1140; over 20: 57.
15. 26,200, 20,100
Everyone gets the same amount, so the mean and median both go up by 1200: 25000 + 1200 = 26200, 18900 + 1200 = 20100.
16. True
The mean stays only if the new value equals the old mean, 69; the new singer is 69.
17. False
The mean stays only if the new value equals the old mean, 70; the new singer is 67.
18. 77°F
Every value is multiplied by 1.8 and has 32 added, so the mean too: 1.8 × 25 + 32 = 77.

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