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1a. [2 marks]

The final examination results obtained by a group of 3200 Biology students are summarized on the

cumulative frequency graph.

Find the median of the examination results.

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1b. [3 marks]

Find the interquartile range.

1c. [2 marks]

350 of the group obtained the highest possible grade in the examination.

Find the final examination result required to obtain the highest possible grade.

1d. [2 marks]

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The grouped frequency table summarizes the examination results of this group of students.

Write down the modal class.

1e. [1 mark]

Write down the mid-interval value of the modal class.

1f. [2 marks]

Calculate an estimate of the mean examination result.

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1g. [1 mark]

Calculate an estimate of the standard deviation, giving your answer correct to three decimal places.

1h. [3 marks]

The teacher sets a grade boundary that is one standard deviation below the mean.

Use the cumulative frequency graph to estimate the number of students whose final examination result

was below this grade boundary.

2a. [1 mark]

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In a high school, 160 students completed a questionnaire which asked for the number of people they

are following on a social media website. The results were recorded in the following box-and-whisker

diagram.

Write down the median.

2b. [2 marks]

The following incomplete table shows the distribution of the responses from these 160 students.

Complete the table.

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2c. [1 mark]

Write down the mid-interval value for the 100 < x ≤ 150 group.

2d. [2 marks]

Using the table, calculate an estimate for the mean number of people being followed on the social media

website by these 160 students.

3a. [1 mark]

The histogram shows the time, t, in minutes, that it takes the customers of a restaurant to eat their

lunch on one particular day. Each customer took less than 25 minutes.

The histogram is incomplete, and only shows data for 0 ≤ t < 20.

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Write down the mid-interval value for 10 ≤ t < 15.

3b. [1 mark]

The mean time it took all customers to eat their lunch was estimated to be 12 minutes.

It was found that k customers took between 20 and 25 minutes to eat their lunch.

Write down the total number of customers in terms of k.

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3c. [3 marks]

Calculate the value of k.

3d. [1 mark]

Hence, complete the histogram.

4a. [1 mark]

A group of 800 students answered 40 questions on a category of their choice out of History, Science and

Literature.

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For each student the category and the number of correct answers, , was recorded. The results

obtained are represented in the following table.

State whether is a discrete or a continuous variable.

4b. [1 mark]

Write down, for , the modal class;

4c. [1 mark]

Write down, for , the mid-interval value of the modal class.

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4d. [2 marks]

Use your graphic display calculator to estimate the mean of ;

4e. [1 mark]

Use your graphic display calculator to estimate the standard deviation of .

4f. [2 marks]

A test at the 5% significance level is carried out on the results. The critical value for this test is

12.592.

Find the expected frequency of students choosing the Science category and obtaining 31 to 40 correct

answers.

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4g. [1 mark]

Write down the null hypothesis for this test;

4h. [1 mark]

Write down the number of degrees of freedom.

4i. [1 mark]

Write down the -value for the test;

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4j. [2 marks]

Write down the statistic.

4k. [2 marks]

State the result of the test. Give a reason for your answer.

5a. [2 marks]

The lengths of trout in a fisherman’s catch were recorded over one month, and are represented in the

following histogram.12

Complete the following table.

5b. [1 mark]

State whether length of trout is a continuous or discrete variable.

5c. [1 mark]

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Write down the modal class.

5d. [2 marks]

Any trout with length 40 cm or less is returned to the lake.

Calculate the percentage of the fisherman’s catch that is returned to the lake.

6a. [1 mark]

A survey was conducted to determine the length of time, , in minutes, people took to drink their coffee

in a café. The information is shown in the following grouped frequency table.

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Write down the total number of people who were surveyed.

6b. [1 mark]

Write down the mid-interval value for the group.

6c. [2 marks]

Find an estimate of the mean time people took to drink their coffee.

6d. [2 marks]

The information above has been rewritten as a cumulative frequency table.

Write down the value of and the value of .

6e. [4 marks]

This information is shown in the following cumulative frequency graph.

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For the people who were surveyed, use the graph to estimate

(i)     the time taken for the first people to drink their coffee;

(ii)     the number of people who take less than minutes to drink their coffee;

(iii)     the number of people who take more than minutes to drink their coffee.

7a. [1 mark]

Toronto’s annual snowfall, x, in cm, has been recorded for the past 176 years. The results are shown in

the table.

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Write down the modal class.

7b. [1 mark]

Write down the mid interval value for the class 6 ≤ x < 10 .

7c. [2 marks]

Calculate an estimate of the mean annual snowfall.

7d. [2 marks]

Find the number of years for which the annual snowfall was at least 18 cm.

8a. [1 mark]

200 people were asked the amount of time T (minutes) they had spent in the supermarket. The results

are represented in the table below.

State if the data is discrete or continuous.

8b. [1 mark]

State the modal group.

8c. [1 mark]

Write down the midpoint of the interval 10 < T ≤ 20 .

8d. [3 marks]

Use your graphic display calculator to find an estimate for

(i) the mean;

(ii) the standard deviation.

8e. [2 marks]

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The results are represented in the cumulative frequency table below, with upper class boundaries of

10, 20, 30, 40, 50.

Write down the value of

(i) q;

(ii) r.

8f. [4 marks]

The results are represented in the cumulative frequency table below, with upper class boundaries of

10, 20, 30, 40, 50.

On graph paper, draw a cumulative frequency graph, using a scale of 2 cm to represent 10 minutes (T)

on the horizontal axis and 1 cm to represent 10 people on the vertical axis.

8g. [6 marks]

Use your graph from part (f) to estimate

(i) the median;

(ii) the 90th percentile of the results;

(iii) the number of people who shopped at the supermarket for more than 15 minutes.

9a. [1 mark]

The speed, , in , of vehicles passing a point on the road was measured. The results are

given below.

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Write down the midpoint of the interval.

9b. [3 marks]

Use your graphic display calculator to find an estimate for

(i)     the mean speed of the vehicles;

(ii)     the standard deviation of the speeds of the vehicles.

9c. [1 mark]

Write down the number of vehicles whose speed is less than or equal to .

9d. [2 marks]

Consider the cumulative frequency table below.

Write down the value of , of and of .

9e. [4 marks]

Consider the cumulative frequency table below.

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Draw a cumulative frequency graph for the information from the table. Use cm to represent

on the horizontal axis and cm to represent vehicles on the vertical axis.

 

9f. [4 marks]

Use your cumulative frequency graph to estimate

(i)     the median speed of the vehicles;

(ii)     the number of vehicles that are travelling at a speed less than or equal to .

9g. [3 marks]

All drivers whose vehicle’s speed is greater than one standard deviation above the speed limit of

will be fined.

Use your graph to estimate the number of drivers who will be fined.

10a. [1 mark]

The weights of 90 students in a school were recorded. The information is displayed in the following

table.

Write down the mid interval value for the interval .

10b. [2 marks]

Use your graphic display calculator to find an estimate for the mean weight.

10c. [1 mark]

Use your graphic display calculator to find an estimate for the standard deviation.

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10d. [2 marks]

Find the weight that is 3 standard deviations below the mean.

11a. [3 marks]

120 Mathematics students in a school sat an examination. Their scores (given as a percentage) were

summarized on a cumulative frequency diagram. This diagram is given below.

Complete the grouped frequency table for the students.

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11b. [1 mark]

Write down the mid-interval value of the interval.

11c. [2 marks]

Calculate an estimate of the mean examination score of the students.

12a. [1 mark]

The diagram shows the cumulative frequency graph for the time t taken to perform a certain task by

2000 men.

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Use the diagram to estimate the median time.

12b. [2 marks]

Use the diagram to estimate the upper quartile and the lower quartile.

12c. [1 mark]

Use the diagram to estimate the interquartile range.

12d. [3 marks]

Find the number of men who take more than 11 seconds to perform the task.

12e. [2 marks]

55 % of the men took less than p seconds to perform the task. Find p.

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12f. [1 mark]

The times taken for the 2000 men were grouped as shown in the table below.

Write down the value of a.

12g. [1 mark]

The times taken for the 2000 men were grouped as shown in the table below.

Write down the value of b.

12h. [2 marks]

Use your graphic display calculator to find an estimate of the mean time.

12i. [1 mark]

Use your graphic display calculator to find an estimate of the standard deviation of the time.

12j. [3 marks]

Everyone who performs the task in less than one standard deviation below the mean will receive a

bonus. Pedro takes 9.5 seconds to perform the task.

Does Pedro receive the bonus? Justify your answer.

13a. [2 marks]

The distribution of the weights, correct to the nearest kilogram, of the members of a football club is

shown in the following table.

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On the grid below draw a histogram to show the above weight distribution.

13b. [1 mark]

Write down the mid-interval value for the interval.

13c. [2 marks]

Find an estimate of the mean weight of the members of the club.

13d. [1 mark]

Write down an estimate of the standard deviation of their weights.

14a. [3 marks]

The table below shows the number of words in the extended essays of an IB class.

Draw a histogram on the grid below for the data in this table.

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14b. [1 mark]

Write down the modal group.

14c. [2 marks]

The maximum word count is words.

Write down the probability that a student chosen at random is on or over the word count.

15a. [1 mark]

The following histogram shows the weights of a number of frozen chickens in a supermarket. The

weights are grouped such that , and so on.

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Find the total number of chickens.

15b. [1 mark]

Write down the modal group.

15c. [2 marks]

Gabriel chooses a chicken at random.

Find the probability that this chicken weighs less than .

16a. [1 mark]

A random sample of 167 people who own mobile phones was used to collect data on the amount of

time they spent per day using their phones. The results are displayed in the table below.

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State the modal group.

16b. [3 marks]

Use your graphic display calculator to calculate approximate values of the mean and standard deviation

of the time spent per day on these mobile phones.

16c. [4 marks]

On graph paper, draw a fully labelled histogram to represent the data.

16d. [3 marks]

Manuel conducts a survey on a random sample of 751 people to see which television programme type

they watch most from the following: Drama, Comedy, Film, News. The results are as follows.

Manuel decides to ignore the ages and to test at the 5 % level of significance whether the most watched

programme type is independent of gender.

Draw a table with 2 rows and 4 columns of data so that Manuel can perform a chi-squared test.

16e. [1 mark]

State Manuel’s null hypothesis and alternative hypothesis.

16f. [2 marks]

Find the expected frequency for the number of females who had ‘Comedy’ as their most-watched

programme type. Give your answer to the nearest whole number.

16g. [3 marks]

Using your graphic display calculator, or otherwise, find the chi-squared statistic for Manuel’s data.

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16h. [3 marks]

(i) State the number of degrees of freedom available for this calculation.

(ii) State his conclusion.

17a. [2 marks]

The figure below shows the lengths in centimetres of fish found in the net of a small trawler.

Find the total number of fish in the net.

17b. [5 marks]

Find (i) the modal length interval,

(ii) the interval containing the median length,

(iii) an estimate of the mean length.

17c. [3 marks]

(i) Write down an estimate for the standard deviation of the lengths.

(ii) How many fish (if any) have length greater than three standard deviations above the mean?

17d. [2 marks]

The fishing company must pay a fine if more than 10% of the catch have lengths less than 40cm.

Do a calculation to decide whether the company is fined.29

17e. [2 marks]

A sample of 15 of the fish was weighed. The weight, W was plotted against length, L as shown below.

Exactly two of the following statements about the plot could be correct. Identify the two correct

statements.

Note: You do not need to enter data in a GDC or to calculate r exactly.

(i) The value of r, the correlation coefficient, is approximately 0.871.

(ii) There is an exact linear relation between W and L.

(iii) The line of regression of W on L has equation W = 0.012L + 0.008 .

(iv) There is negative correlation between the length and weight.

(v) The value of r, the correlation coefficient, is approximately 0.998.

(vi) The line of regression of W on L has equation W = 63.5L + 16.5.

18a. [2 marks]

Consider the frequency histogram for the distribution of the time, , in minutes of telephone calls that

Helen made last week.

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Complete the frequency table for this distribution.

18b. [1 mark]

Write down the modal class.

18c. [1 mark]

Write down the mid interval value of the class.

18d. [2 marks]

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Use your graphic display calculator to find an estimate for the mean time.

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