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IB Mathematics: Applications and Interpretation SL · 13.3: Statistics · 13.3.2

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Spread and standard deviation Problem set B

Show your working. Use the calculator's σx for the standard deviation, and give answers to 3 significant figures.

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 mean absolute deviation of 5, 8, 9, 15, 18.

  2. The deviations from the mean of a data set of five values are −7, −1, 2, 3, 3.

    1. (a) Find the variance.
    2. (b) Find the standard deviation.

  3. A basketball player scored 54, 47, 62, 41, 56 points in five games.

    1. (a) Find the mean.
    2. (b) Complete a table of deviations and squared deviations, and find the sum of the squared deviations.
    3. (c) Find the standard deviation.

  4. Two bakeries weighed eight loaves each. The dot plot shows the masses, in grams. Bakery 1: 497, 498, 500, 500, 500, 500, 502, 503 Bakery 2: 491, 494, 497, 500, 500, 503, 506, 509

    489492495498501504507510513Bakery 2Bakery 1
    1. (a) Show that both have the same mean.
    2. (b) Use your calculator to find the standard deviation of each.
    3. (c) Which is more spread out? Give a reason.

  5. The heights of a type of sunflower, in cm, are roughly bell-shaped with mean 140 and standard deviation 12.

    96108120132144156168180Height (cm)
    1. (a) What percentage lie between 128 and 152?
    2. (b) What percentage lie between 116 and 164?
    3. (c) What percentage lie above 176?

In context

  1. Five people each assembled a flat-pack kit. Their times, in minutes, were 62, 58, 65, 60, 60. The fastest known time is 54 minutes.

    1. (a) Find the mean.
    2. (b) Find the standard deviation.
    3. (c) How many standard deviations below the mean is the fastest known time?

  2. Five journey times, in minutes, are 18, 22, 25, 27, 33.

    1. (a) Find the mean and standard deviation of the original data.
    2. (b) Roadworks add 6 minutes to every journey. Find the new mean and standard deviation.
    3. (c) On a slow bus, every journey takes exactly 2 times as long as the original. Find the new mean and standard deviation.
    4. (d) Describe what happens to the mean and to the standard deviation in each case.

  3. Eight students swam one length of a pool. Their times, in seconds, are 31, 33, 34, 36, 37, 39, 40, 42. The last time is typed into a computer as 420 instead of 42.

    1. (a) Find the mean and standard deviation of the correct data.
    2. (b) Find the mean and standard deviation of the data with the error.
    3. (c) Find the median and IQR of both sets of data.
    4. (d) Explain which measures of average and spread you would use for the data with the error.

Stretch

  1. Two bakers cut baguettes. The lengths of five baguettes from each baker, in cm, are Baker 1: 37, 39, 40, 41, 43 Baker 2: 36, 40, 40, 40, 44

    1. (a) Show that both have the same mean and the same mean absolute deviation.
    2. (b) Find the standard deviation of each.
    3. (c) Which is more consistent? Explain why MAD did not show the difference.

  2. The masses of 400 lemons, in grams, are roughly bell-shaped with mean 120 and standard deviation 9.

    1. (a) About how many have a value between 111 and 129?
    2. (b) About how many have a value above 138?
    3. (c) Between which two values do the middle 95% lie?

jmaths.xyz · AI SL · 13.3.2 Spread and standard deviation