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

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Statistics review Problem set B

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

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. State whether each is discrete or continuous data.

    1. (a) The masses of bags of flour.
    2. (b) The number of siblings a student has.
    3. (c) The temperature at noon.
    4. (d) The number of pages in a book.

  2. The table shows the number of brothers and sisters of each student in a class.

    Siblings012345Frequency6117421
    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 distances, in metres, thrown by 80 athletes in a javelin competition.

    1520253035404550556065707580Distance (m)
    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 mean delivery time, in minutes, of a pizza shop on each of 120 days is summarised in the box plot.

    Time1015202530354045505560Delivery time (min)
    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 25 and 30 minutes.
    5. (e) Write down the number of days with between 25 and 55 minutes.
    6. (f) On a day with a road closure the mean delivery time was 60 minutes. Determine whether this day is an outlier.

  2. The table shows the number of parcels delivered to each of 48 houses on a street in one week.

    Parcels01234Frequency4816128
    1. (a) State whether the number of parcels 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 12 houses is taken, using the number of parcels as the strata. Find how many houses in the sample had 2 parcels.

  3. The number of emails received by a manager on each of 14 days was: 34, 41, 28, 52, 45, 38, 31, 49, 36, 44, 29, 95, 40, 33

    1. (a) Find the median and the lower and upper quartiles.
    2. (b) Find the interquartile range.
    3. (c) Show that 95 is an outlier.
    4. (d) Find the mean of the values that are not outliers.

Stretch

  1. A hiker records the height above sea level, x hundred metres, and the air temperature, y °C, at eight points on a mountain path. x: 2.1, 3.4, 4.5, 5.2, 6.3, 7.4, 8, 9.1 y: 11.4, 8.9, 7.2, 6.8, 3.9, 2.1, 0.8, −1.5

    246810510xy
    1. (a) State whether the air temperature 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 air temperature when the height is 6.
    5. (e) Interpret the gradient of the line.
    6. (f) Explain why the line should not be used when the height is 30 hundred metres.

  2. The daily steps, in hundreds, of two walking groups, each recorded over 80 days, are shown in the box plots.

    Group MGroup N3035404550556065707580859095100105Steps (hundreds)
    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 days in Group M with a number of steps between 65 and 80.
    4. (d) One more day is recorded for Group N with a number of steps of 100. Determine whether this is an outlier for Group N.
    5. (e) Compare the spread of the two groups.

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