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Measures of central tendency

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Written by Dr. Nadia Shah (Statistics)

12 Class 11 Statistics questions with answers and explanations.

Printable worksheet with answer key

All questions with answers
  1. The arithmetic mean of 2, 4, 6, 8 and 10 is:

    • 1 8
    • 2 6
    • 3 5
    • 4 30
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    Correct answer: 6

    The sum is 30 and there are 5 values, so 30 ÷ 5 = 6.

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  2. The median of 3, 5, 7, 9 and 11 is:

    • 1 7
    • 2 35
    • 3 5
    • 4 9
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    Correct answer: 7

    The middle value of the five ordered values is 7.

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  3. The median of 4, 6, 8 and 10 is:

    • 1 7
    • 2 28
    • 3 8
    • 4 6
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    Correct answer: 7

    With an even number of values the median is the mean of 6 and 8, which is 7.

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  4. The mode of 2, 3, 3, 4, 3, 5 is:

    • 1 5
    • 2 2
    • 3 3
    • 4 4
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    Correct answer: 3

    3 occurs three times, more than any other value.

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  5. Which average is least affected by extreme values?

    • 1 The sum
    • 2 The weighted mean
    • 3 The median
    • 4 The mean
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    Correct answer: The median

    The median depends only on the middle position.

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  6. The formula for the mean of a frequency distribution is:

    • 1 Σx × Σf
    • 2 Σx ÷ Σf
    • 3 Σf ÷ Σfx
    • 4 Σfx ÷ Σf
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    Correct answer: Σfx ÷ Σf

    Multiply each value by its frequency, add them and divide by the total frequency.

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  7. A set of data with two modes is called:

    • 1 Unimodal
    • 2 Skewed
    • 3 Bimodal
    • 4 Symmetric
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    Correct answer: Bimodal

    Two values with the highest frequency make the data bimodal.

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  8. Which average can be used for non-numerical data such as favourite colours?

    • 1 The mean
    • 2 The mode
    • 3 The weighted mean
    • 4 The median
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    Correct answer: The mode

    The mode is the most frequent category.

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  9. The mean of 10, 20 and 30 is:

    • 1 60
    • 2 20
    • 3 30
    • 4 10
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    Correct answer: 20

    The sum is 60 and 60 ÷ 3 = 20.

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  10. The sum of 5 values is 40. Their mean is:

    • 1 5
    • 2 35
    • 3 8
    • 4 200
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    Correct answer: 8

    40 ÷ 5 = 8.

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  11. A weighted mean is used when:

    • 1 There is only one value
    • 2 The values have different importance
    • 3 The data are not numbers
    • 4 All values are equal
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    Correct answer: The values have different importance

    Each value is multiplied by its weight.

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  12. The mean of the frequency distribution with values 1, 2 and 3 and frequencies 2, 3 and 5 is:

    • 1 2.3
    • 2 2
    • 3 1.5
    • 4 3
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    Correct answer: 2.3

    Σfx = 2 + 6 + 15 = 23 and Σf = 10, so the mean is 2.3.

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