Practice questions 7.1


1. Find (a) the modal group, (b) the median group and (c) the estimated mean, correct to two decimal places, of the following grouped frequency tables. (i) Time (min)


No. of people (ii) Cost (€) No. of people (iii) Days missed No. of students (iv) Books read No. of people


0–10 10–20 20–30 30–40 40–50 3


12 8 Note: 0–10 means 0 or more but less than 10


20–40 40–60 60–80 80–100 100–120 5


9 16 Note: 20–40 means 20 or more but less than 40


2–4 4–6 6–8 8–10 10–12 22


8 13 Note: 2–4 means 2 or more but less than 4


0–5 5–10 10–15 15–20 20–25 12


9 23 18 16 Note: 0–5 means 0 or more but less than 5


2. The table shows the distance walked by a group of students to get to school. Distance (km)


No. of students


0–0⋅5 0⋅5–1⋅5 1⋅5–2⋅0 2⋅0–2⋅5 30


22 19 8


Note: 0–0⋅5 means 0 or more but less than 0·5 (i) Are the modal group and the median group the same? (ii) Using mid-interval values, estimate the mean, correct to two decimal places. (iii) Is the estimated mean in either the modal or median group?


3. The table shows the amount of money spent by 40 customers in a shop. Amount (€)


No. of customers


0–8 8–12 12–16 16–20 20–32 2


9 13 10 6


Note: 0–8 means 0 or more but less than 8 (i) What is the modal group? (ii) In which group does the median lie? (iii) Use the mid-interval values to estimate the mean of this data. (iv) What is the maximum number of customers that could have spent €25 or more?


4. The grouped frequency table below refers to the marks obtained by 85 students in a test. Marks


No. of students


0–40 40–55 55–70 70–100 16


18 27 24


Note: 0–40 means 0 or more but less than 40 (i) What is the modal interval? (ii) In which interval does the median lie? (iii) What percentage of students got 55 marks or higher? (iv) Estimate the mean mark, to one decimal place, obtained by this group of students.


Section A Applying our skills 131 9 6 11 2 10 3


7 Statistics 2


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