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    PracticeAQA GCSEAQA GCSE Maths Foundation Tier Paper 1 Non-CalculatorQuestion 21.2
    Easy1 markMultiple Choice
    StatisticsStatisticsAveragesMedianFoundation

    AQA GCSE · Question 21.2 · Statistics

    Each number in a list is increased by 10. For the statement "The median is increased by 10", tick one box.

    Answer options:

    A.

    True

    B.

    False

    C.

    Cannot tell

    How to approach this question

    1. **Understand the median:** The median is the middle value when the data is in order. 2. **Consider an example:** Let the ordered list be {2, 3, 5, 8, 9}. The median is the middle value, which is 5. 3. **Apply the change:** Increase each number by 10. The new list is {12, 13, 15, 18, 19}. 4. **Find the new median:** The list is still in order. The new middle value is 15. 5. **Compare:** The original median was 5, the new median is 15. The median has increased by 10 (15 - 5 = 10). 6. **Generalise:** Since every number is increased by 10, the order of the numbers does not change. The number that was in the middle before will still be in the middle, and its value will be 10 greater. So the statement is true.

    Full Answer

    A.True✓ Correct
    True
    The median is the middle value of a data set when it is arranged in numerical order. Let's take an example data set: `S = {1, 3, 6, 8, 9}`. This set is already in order. The middle value is 6. So, the median is 6. Now, let's increase each number in the list by 10 to create a new set, `S`. `S` = {1+10, 3+10, 6+10, 8+10, 9+10} = {11, 13, 16, 18, 19}`. The new set is also in order. The middle value is now 16. So, the new median is 16. The original median was 6, and the new median is 16. The new median is the original median + 10. This is because adding a constant value to every number in a set does not change their order, it simply shifts the entire set along the number line. The middle value will also be shifted by that same constant amount. Therefore, the statement is **True**.

    Common mistakes

    ✗ Confusing median with mean or mode.\n✗ Thinking that the order of the numbers might change.
    Question 21.1All questionsQuestion 21.3

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