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IB Mathematics: Applications and Interpretation HL · 13.3: Statistics · 13.3.3

Name Date

Changing every value Problem set B

Say whether the change is adding or multiplying, then write down the effect on each measure. Use the calculator where data is given.

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. Find the new mean and standard deviation of each data set.

    1. (a) The mean is 72 and the standard deviation is 6.4. Then 18 is added to every value.
    2. (b) The mean is 410 and the standard deviation is 27. Then 90 is subtracted from every value.

  2. Find the new median and IQR.

    1. (a) A data set has median 91 and IQR 24. Every value is decreased by 40.
    2. (b) A data set has median 12.5 and IQR 3.2. Every value is increased by 4.5.

  3. Find the new median and IQR.

    1. (a) A data set has median 9 and IQR 3.5. Every value is multiplied by 8.
    2. (b) A data set has median 260 and IQR 52. Every value is divided by 5.

  4. Find the new mean and standard deviation.

    1. (a) The mean is 16 and the standard deviation is 2.5. Every value is multiplied by 4.
    2. (b) The mean is 36 and the standard deviation is 4.5. Every value is divided by 9.

  5. A data set has standard deviation 1.5. Every value is multiplied by 4. Find the new standard deviation and the new variance.

In context

  1. The scores of a class on a quiz have mean 46, standard deviation 7.5, median 44 and IQR 9. The teacher adds 5 marks to every score. Write down the new mean, standard deviation, median and IQR.

  2. The marks of a class have mean 52 and standard deviation 10. The marks are rescaled: new mark = 1.5 × old mark + 8. Find the mean and standard deviation of the new marks.

  3. A café records how many cups of tea it sells in five hours: 9, 11, 14, 15, 21. Over a festival, sales in each hour are three times as many, plus 2 extra cups.

    1. (a) Find the mean and standard deviation of the original data.
    2. (b) Write down the new data, and find its mean and standard deviation from the calculator.
    3. (c) Find the new mean and standard deviation from the original ones, without the new data, and check they agree.

Stretch

  1. Every value in a data set is multiplied by k (k > 0) and then b is added. The original mean is 20 and the original standard deviation is 4. The new mean is 47 and the new standard deviation is 8. Find k and b.

  2. The journey times of a bus route have mean 30 minutes and standard deviation 5 minutes. New traffic lights make every journey 10% shorter, and a new stop then adds 4 minutes to every journey. Find the mean and standard deviation of the new journey times.

jmaths.xyz · AI HL · 13.3.3 Changing every value