ExpertEasy1 markMultiple Choice
AQA GCSE · Question 21.1 · Statistics
Each number in a list is increased by 10. For the statement "The mode is increased by 10", tick one box.
Each number in a list is increased by 10. For the statement "The mode is increased by 10", tick one box.
Answer options:
A.
True
B.
False
C.
Cannot tell
How to approach this question
1. **Understand the mode:** The mode is the most frequently occurring value in a data set.
2. **Consider an example:** Let the list be {2, 3, 3, 4}. The mode is 3.
3. **Apply the change:** Increase each number by 10. The new list is {12, 13, 13, 14}.
4. **Find the new mode:** The most frequent value in the new list is 13.
5. **Compare:** The original mode was 3, the new mode is 13. The mode has increased by 10 (13 - 3 = 10).
6. **Generalise:** Since every number is increased by 10, the number that was most frequent before will still be the most frequent after the change (just 10 bigger). So the statement is true.
Full Answer
A.True✓ Correct
True
The mode is the value that appears most often in a set of data.
Let's take an example data set: `S = {1, 2, 2, 3, 5}`.
The mode of this set is 2, because it appears twice, more than any other number.
Now, let's increase each number in the list by 10 to create a new set, S.
S = {1+10, 2+10, 2+10, 3+10, 5+10} = {11, 12, 12, 13, 15}`.
The mode of the new set `S is 12, because it appears most frequently.
The original mode was 2, and the new mode is 12. The new mode is the original mode + 10.
This will always be the case. If a certain number is the most common, then when you add 10 to every number, that original number (plus 10) will still be the most common. Therefore, the statement is **True**.
Common mistakes
✗ Getting confused between mode, median, and mean.\n✗ Thinking that adding a constant could change which number is the most frequent.
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