Measures of central tendency · Ages 14–15
How changing the data changes the averages
Add k to all: add k. Multiply all by k: multiply by k.
How to do it
Method
Add k to all: add k. Multiply all by k: multiply by k
Mean 30, each plus 5 then doubled: (30 + 5) × 2 = 70
Another way
Work it out again
Write the new data, then find the mean
In full
Add the same number k to every value: the mean, median and mode all go up by k. Multiply every value by k: all three are multiplied by k. Put in a value: above the old mean, the mean rises; below it, it falls; equal to it, it stays. The median has to be found again from the new order. Taking a value out works the same, the other way. One way: write the new data down and work everything out again. Another: reason from the rules, so 10 numbers with mean 30, each increased by 5 and then doubled, have the new mean (30 + 5) × 2 = 70 without working through them. Mind the order: adding then multiplying is not multiplying then adding.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A team's 4 players have a mean weight of 44 kg. A new player of 56 kg joins. What is the mean weight of the 5, in kg?
Show the answer and working
Answer: 46.4 kg
The old total is 4 × 44 = 176; with the new player 176 + 56 = 232; over 5: 46.4 kg.
Example 2
9 data have a mean of 54. The value 52 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
Show the answer and working
Answer: D. It falls
Compare 52 with the old mean 54: above it, the mean rises; below, it falls; equal, it stays.
Example 3
26 data have a mean of 23. Each value has 7 added, then is multiplied by 2. What is the new mean?
Show the answer and working
Answer: 60
In order: adding 7 makes the mean 23 + 7 = 30; times 2: 30 × 2 = 60.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.25 items have a mean price of $186. Every price goes up by $11. What is the new mean price, in dollars?
Answer:
2.5 data have a mean of 47. The value 42 is put in. What happens to the mean?
- A. It rises
- B. It stays the same
- C. It can't be told
- D. It falls
Choose the right answer
Answer:
3.A team's 4 players have a mean weight of 48 kg. A new player of 46 kg joins. What is the mean weight of the 5, in kg?
Answer:
4.26 data have a mean of 37. Each value has 5 added, then is multiplied by 3. What is the new mean?
Answer:
5.19 data have a median of 49. Each value is multiplied by 2, then has 6 taken away. The new median is 92.
True or false?
Answer:
All the answers
- 1. 197 dollars
- 2. D. It falls
- 3. 47.6 kg
- 4. 126
- 5. True
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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