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IB Mathematics: Applications and Interpretation SL · 13.3: Statistics · 13.3.9

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Statistics review Problem set A

Use the calculator for means, standard deviations, quartiles and regression. Give answers to 3 significant figures unless they are exact.

Difficulty: first skills applying them stretch

Skills

  1. State whether each is discrete or continuous data.

    1. (a) The heights of seedlings.
    2. (b) The number of goals in a match.
    3. (c) The time taken to run 100 m.
    4. (d) The number of rooms in a hotel.

  2. The table shows the number of goals scored by a team in each match of a season.

    Goals012345Frequency4912731
    1. (a) Write down the total frequency.
    2. (b) Write down the mode.
    3. (c) Find the mean.
    4. (d) Find the standard deviation.

  3. The box plot shows the times, in seconds, taken by 50 players to finish a puzzle.

    253035404550556065707580859095Time (s)
    1. (a) Write down the median.
    2. (b) Write down the minimum.
    3. (c) Find the interquartile range.
    4. (d) Find the range.

In context

  1. The number of visitors to a museum on each of 160 days is summarised in the box plot.

    Visitors120140160180200220240260280300320340360380400420440460480500Visitors
    1. (a) Write down the median.
    2. (b) Write down the maximum.
    3. (c) Find the interquartile range.
    4. (d) Write down the number of days with between 210 and 260 visitors.
    5. (e) Write down the number of days with between 210 and 470 visitors.
    6. (f) A storm closed most of the museum on one day and only 25 people visited. Determine whether this day is an outlier.

  2. The table shows the number of days that each of 60 students was absent last term.

    Days absent0123456Frequency691512963
    1. (a) State whether the number of days absent is discrete or continuous.
    2. (b) Write down the total frequency and the mode.
    3. (c) Find the mean and the standard deviation.
    4. (d) A stratified sample of 20 students is taken, using the number of days absent as the strata. Find how many students in the sample had 3 days absent.

  3. The daily rainfall, in mm, was recorded on 14 days: 2.1, 0, 3.4, 1.2, 5.6, 2.8, 0.5, 4.1, 3, 2.2, 1.5, 18.6, 3.9, 2.4

    1. (a) Find the median and the lower and upper quartiles.
    2. (b) Find the interquartile range.
    3. (c) Show that 18.6 is an outlier.
    4. (d) Find the mean of the values that are not outliers.

Stretch

  1. A kiosk records the maximum temperature, x °C, and the number of bottles of water, y, sold on each of eight days. x: 18, 21, 24, 27, 30, 32, 25, 29 y: 62, 70, 88, 95, 120, 128, 85, 110

    2025306080100120xy
    1. (a) State whether the number of bottles sold is discrete or continuous.
    2. (b) Find Pearson's correlation coefficient r and describe the correlation.
    3. (c) Find the equation of the regression line of y on x.
    4. (d) Use the equation to estimate the number of bottles sold when the temperature is 26.
    5. (e) Interpret the gradient of the line.
    6. (f) Explain why the line should not be used when the temperature is 40 °C.

  2. The scores of two classes in a test, 60 students in each class, are shown in the box plots.

    Class PClass Q20253035404550556065707580859095Score
    1. (a) Write down the median of each group. Which group has the higher median?
    2. (b) Find the interquartile range of each group.
    3. (c) Write down the number of students in Class P with a score between 60 and 70.
    4. (d) One more student joins Class P with a score of 10. Determine whether this is an outlier for Class P.
    5. (e) Compare the spread of the two groups.

jmaths.xyz · AI SL · 13.3.9 Statistics review: exam questions