Name: ____________________
Statistics - Unit 2 Level 3
1a. [1 mark] The diagram shows the cumulative
frequency graph for the time t taken to perform a
certain task by 2000 men. Use the diagram to
estimate the median time.
1b. [2 marks] Use the diagram to estimate the
upper quartile and the lower quartile.
1c. [1 mark] Use the diagram to estimate the
interquartile range.
1d. [3 marks] Find the number of men who take
more than 11 seconds to perform the task.
1e. [2 marks] 55 % of the men took less than p
seconds to perform the task. Find p.
1f. [2 mark] The times taken for the 2000 men were grouped as
shown in the table below. Write down the value of a.
1g. [1 mark] State the modal class.
1h. [2 mark] The times taken for the 2000 men were grouped as shown in the table below. Write down the
value of b.
1i. [3 marks] One man who arrived late and is not represented on the graph took 27 seconds to complete the
task. Determine if this time is an outlier, justify your answer with a calculation.
1
2a. [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.
On the grid below draw a histogram to show the above weight distribution.
2b. [2 marks] Write down the mid-interval value for the 40-49 interval with calculation.
2c. [2 marks] Hence find an estimate of the mean weight of the members of the club with calculation.
2d. [1 mark] Write down an estimate of the standard deviation of their weights.
2
3a. [2 marks]
The grades obtained by a group of IB students are listed below:
Complete the following table for the grades obtained by the students.
3b. [1 mark] Write down the mode grade obtained by the students.
3c. [2 marks] Calculate the median grade obtained by the students.
3d. [2 marks] Calculate the mean grade obtained by the students.
3e. Calculate the standard deviation for the class scores
3f. Anyone who scored 1 standard deviation above the mean gets a gold star. How many people in the class
will receive gold stars? Justify your answer.
3
Two groups of 40 students were asked how many books they had read in the last two months.
The results for group 1 are shown in the frequency table.
4a. [1 mark] Determine the median number of books read
4b. [3 marks] Determine the interquartile range for the
number of books read
4c. [5 marks] Draw a box and whisker plot for the number of books read by group 1
4d. [2 marks] The results for the Group 2, are shown in the box and whisker plot below. Estimate the
number of students in Group 2, that have read at least 6 books.
4e. [4 marks] Compare the box and whisker plots of both groups. Based on what you see, which class would
have a higher standard deviation? In your own words explain what standard deviation means and explain why
you chose your answer.
