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

Name Date

Changing every value Problem set A

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

Difficulty: first skills applying them stretch

Skills

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

    1. (a) The mean is 58 and the standard deviation is 9.5. Then 15 is added to every value.
    2. (b) The mean is 240 and the standard deviation is 31. Then 65 is subtracted from every value.

  2. Find the new median and IQR.

    1. (a) A data set has median 63 and IQR 17. Every value is decreased by 25.
    2. (b) A data set has median 7.8 and IQR 2.4. Every value is increased by 3.5.

  3. Find the new median and IQR.

    1. (a) A data set has median 14 and IQR 5. Every value is multiplied by 6.
    2. (b) A data set has median 90 and IQR 36. Every value is divided by 4.

  4. Find the new mean and standard deviation.

    1. (a) The mean is 25 and the standard deviation is 4. Every value is multiplied by 3.
    2. (b) The mean is 7.5 and the standard deviation is 0.8. Every value is divided by 5.

  5. A data set has standard deviation 3.2. Every value is multiplied by 5. Find the new standard deviation and the new variance.

In context

  1. The monthly pay of the workers in a factory, in euros, has mean 2800, standard deviation 350, median 2650 and IQR 400. Every worker gets a rise of 150 euros a month. Write down the new mean, standard deviation, median and IQR.

  2. The daily temperatures in a town have mean 22 °C and standard deviation 3.5 °C. To change a temperature to °F, multiply by 1.8 and add 32. Find the mean and standard deviation in °F.

  3. A teacher records how many minutes five students spend on homework: 14, 18, 19, 23, 26. Each student's time is doubled by the end of term and then 3 minutes are added.

    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 12 and the original standard deviation is 3. The new mean is 39 and the new standard deviation is 9. Find k and b.

  2. The prices of the items in a shop have mean \$14 and standard deviation \$2. A sale takes 20% off every price. Delivery then adds \$3 to every item. Find the mean and standard deviation of the final prices.

jmaths.xyz · AI HL · 13.3.3 Changing every value