Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-hl/statistics/13-3-4/problems/b/

jmaths

IB Mathematics: Applications and Interpretation HL · 13.3: Statistics · 13.3.4

Name Date

Quartiles, box plots and outliers Problem set B

Find quartiles from the calculator (median of each half) and show the working. Give means to 2 decimal places and standard deviations to 3 significant figures unless told otherwise.

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 of 46, 52, 41, 49, 55, 44, 51. Give your answer to 2 decimal places.

  2. Find the median of 42, 37, 51, 45, 39, 48, 35, 44, 50.

  3. For the data 34, 41, 29, 52, 38, 45, 31, 47, 36, 50, 43:

    1. (a) write down the five-number summary;
    2. (b) find the interquartile range.

  4. Two data sets are given. The first is 66, 58, 75, 71, 90, 62, 80, 69, 84, 73. The second has five-number summary 6, 13, 18, 26, 35.

    1. (a) Find the five-number summary of the first data set.
    2. (b) State the IQR of the second data set.

  5. Find the population standard deviation of 4, 6, 9, 12, 14, by hand. Give your answer to 3 significant figures.

  6. Ten days have rainfall in millimetres: 41.3, 38.9, 44.2, 40.6, 43.5, 39.8, 42.7, 45.1, 37.4, 42.1. Use a spreadsheet to find the mean and the population standard deviation, each to 2 decimal places.

  7. A data set has Q1 = 28 and Q3 = 44.

    1. (a) Find the lower and upper fences for outliers.
    2. (b) Which of 3, 66 and 70 are outliers?

  8. Use the 1.5 × IQR rule to identify any outliers in 57, 49, 18, 56, 54, 95, 53, 47, 52, 50.

In context

  1. The numbers of emails an office receives on seven days are 24, 31, 27, 29, 22, 26, 140.

    1. (a) Find the mean, to 2 decimal places, and the median.
    2. (b) Which is the better measure of the centre? Give a reason.

  2. Box plots show the time, in minutes, that two classes took to finish a puzzle. Class P: 2, 6, 9, 14, 18. Class Q: 4, 7, 9, 11, 15 (five-number summaries).

    Class PClass Q02468101214161820Time to finish (min)
    1. (a) Find the IQR of each data set.
    2. (b) Compare the two data sets, using the medians and the IQRs.

  3. A baker weighs 11 loaves and records their masses in grams: 402, 398, 405, 401, 399, 404, 400, 397, 403, 406, 455.

    1. (a) Use the 1.5 × IQR rule to find any outliers.
    2. (b) Suggest a possible reason for the unusual value.

  4. A gym records the number of visitors in each of 12 hours: 64, 112, 58, 70, 66, 60, 68, 55, 52, 63, 57, 61. Show that there is an outlier, then draw a box plot.

  5. A bakery counts the burnt loaves in each of 32 batches.

    Burnt loaves01234567Frequency961010141
    1. (a) Find the median.
    2. (b) Find the lower quartile, the upper quartile and the interquartile range.
    3. (c) Show that a batch with 6 burnt loaves is an outlier.

Stretch

  1. Box plots show the masses, in grams, of two batches of fish. The cross on Batch 1 is at 55.

    ×Batch 1Batch 2202530354045505560Mass (g)
    1. (a) Write down the median and the IQR of Batch 1.
    2. (b) Show that the cross on Batch 1 is an outlier.
    3. (c) Compare the masses of the two, using the median and the IQR.
    4. (d) Describe the skew of Batch 1 and say how its mean and median compare.

  2. The nine values 63, 70, 65, 67, 72, 61, 75, 58, 54 are given. A tenth value x is added, and x is larger than all nine. Find the smallest whole number x for which x is an outlier, by the 1.5 × IQR rule.

jmaths.xyz · AI HL · 13.3.4 Quartiles, box plots and outliers