StatisticsAQA GCSE Maths: Topic test

20 questions, 52 marks

AQA GCSE Maths

Statistics topic test

Total 52 marks

Name

Class

Date

1
A gym records the type of exercise class chosen by $60$ members one evening: $21$ chose spin, $15$ chose yoga, $18$ chose HIIT, and the rest chose Pilates.
(a)
(a) How many members chose Pilates?
[1 mark]
A $9$
B $6$
C $3$
D $12$
(b)
(b) If this data were displayed as a pie chart, what angle would represent the spin class?
[1 mark]
A $90^\circ$
B $108^\circ$
C $126^\circ$
D $84^\circ$
(c)
(c) Which type of statistical diagram would be most appropriate for comparing the number of members choosing each exercise class?
[1 mark]
AScatter graph
BHistogram
CCumulative frequency graph
DBar chart
Total for question 1: 3 marks
2
A researcher wants to find the average number of hours per week that people in a large city spend exercising. She stands outside one gym on a Saturday morning and asks the first $40$ people who leave.
(a)
(a) Explain one reason why this sampling method may produce biased results.
[2 marks]
(b)
(b) Suggest one improvement to the sampling method that would make the results more representative.
[2 marks]
Total for question 2: 4 marks
3
The ages, in years, of $11$ people at a coding club meeting are: $12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 21$ .
(a)
(a) Find the median and the interquartile range of these ages.
[3 marks]
(b)
(b) A 12th person joins the club, aged $45$ . Explain what effect, if any, this will have on the median compared with its effect on the range, and justify your answer.
[3 marks]
Total for question 3: 6 marks
4
A teacher records the number of hours, $h$ , spent reading last term by each of $24$ students in her class: $0 \le h < 3$ : $4$ students; $3 \le h < 6$ : $8$ students; $6 \le h < 12$ : $8$ students; $12 \le h < 21$ : $4$ students.
(a)
(a) Use midpoints to estimate the mean number of hours read per student.
[4 marks]
(b)
(b) Calculate the frequency density for the class $6 \le h < 12$ , and state which class interval has the tallest bar on a histogram of this data.
[4 marks]
(c)
(c) The teacher adds a fifth class, $21 \le h < 30$ , containing $2$ more students who read even more. Calculate the frequency density of this new class, and state, with a reason, whether it changes your answer to part (b) about which interval has the tallest bar.
[5 marks]
Total for question 4: 13 marks
5
A school wants to survey students about their lunch preferences. It plans to select every 5th name from an alphabetical list of all $400$ students on the school roll.
(a)
(a) What is this sampling method called?
[1 mark]
ACluster sampling
BStratified sampling
CSystematic sampling
DOpportunity sampling
(b)
(b) How many students would be selected using this method?
[1 mark]
A $5$
B $20$
C $100$
D $80$
(c)
(c) The school has $220$ girls and $180$ boys. If a stratified sample of $40$ students were taken instead, how many boys would be included?
[1 mark]
A $18$
B $22$
C $20$
D $16$
Total for question 5: 3 marks
6
The daily maximum temperatures, in $^\circ C$ , recorded in a town over $7$ days were: $19, 22, 18, 25, 21, 20, 22$ .
(a)
(a) Find the range and the mean of these temperatures.
[2 marks]
(b)
(b) A weather forecaster claims, \"the temperature varied by more than $30\%$ around the mean this week.\" Determine, using the range and mean from part (a), whether this claim is correct.
[2 marks]
Total for question 6: 4 marks
7
Two rival delivery companies, Company P and Company Q, each deliver $200$ parcels in a week. Company P has a median delivery time of $24$ hours and an interquartile range of $6$ hours. Company Q has a median delivery time of $27$ hours and an interquartile range of $14$ hours.
(a)
(a) Compare the two companies' delivery times, referring to both the median and the interquartile range.
[3 marks]
(b)
(b) A customer needs a parcel delivered reliably within a guaranteed time window. Based on the data, explain which company they should choose, justifying your answer using the interquartile range.
[3 marks]
Total for question 7: 6 marks
8
A market stall owner recorded the number of umbrellas sold and the rainfall, in mm, on $8$ randomly chosen days. Rainfall (mm): $2, 5, 8, 3, 10, 6, 1, 9$ . Umbrellas sold: $3, 9, 14, 6, 17, 11, 2, 15$ .
(a)
(a) Describe the type of correlation you would expect between rainfall and umbrella sales, and state, with a reason, whether this data proves that rainfall causes higher umbrella sales.
[4 marks]
(b)
(b) Using the data as a guide, estimate the number of umbrellas that would be sold on a day with $7$ mm of rainfall, and state one reason why this estimate is or is not reliable.
[4 marks]
(c)
(c) Of the $8$ days recorded, $3$ were weekend days with rainfall $8, 10$ and $9$ mm and umbrella sales $14, 17$ and $15$ . Calculate the mean rainfall and mean umbrella sales for the weekend days only, and compare these with the means for all $8$ days, commenting on what this suggests about weekend sales.
[5 marks]
Total for question 8: 13 marks

End of questions