ExpertEasy1 markMultiple Choice
AQA GCSE · Question 21.3 · Statistics
Each number in a list is increased by 10. For the statement "The range is increased by 10", tick one box.
Each number in a list is increased by 10. For the statement "The range is increased by 10", tick one box.
Answer options:
A.
True
B.
False
C.
Cannot tell
How to approach this question
1. **Understand the range:** The range is the difference between the highest and lowest values.
2. **Consider an example:** Let the list be {2, 3, 5, 9}. The lowest value is 2, the highest is 9. The range is 9 - 2 = 7.
3. **Apply the change:** Increase each number by 10. The new list is {12, 13, 15, 19}.
4. **Find the new range:** The new lowest value is 12, the new highest is 19. The new range is 19 - 12 = 7.
5. **Compare:** The original range was 7, the new range is 7. The range has not changed.
6. **Generalise:** The range is (highest value) - (lowest value). The new range is (highest value + 10) - (lowest value + 10) = highest value + 10 - lowest value - 10 = highest value - lowest value. The range stays the same. The statement is false.
Full Answer
B.False✓ Correct
False
The range of a data set is the difference between the maximum value and the minimum value.
Let's take an example data set: `S = {1, 3, 6, 8, 9}`.
The maximum value is 9 and the minimum value is 1.
The range = 9 - 1 = 8.
Now, let's increase each number in the list by 10 to create a new set, `S`.
`S = {11, 13, 16, 18, 19}`.
In the new set, the maximum value is 19 and the minimum value is 11.
The new range = 19 - 11 = 8.
The range has not changed.
Algebraically, if the original max is `M` and the original min is `m`, the range is `M - m`.
After adding 10 to every number, the new max is `M + 10` and the new min is `m + 10`.
The new range is `(M + 10) - (m + 10) = M + 10 - m - 10 = M - m`.
The range is unchanged. Therefore, the statement "The range is increased by 10" is **False**.
Common mistakes
✗ Thinking that because all the numbers increase, the spread must also increase.\n✗ Confusing range with one of the averages.
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