Question
The table shows the height, in metres, above sea-level and the temperature, in °C, at midday for some
places on a mountain.
(a) Complete the scatter diagram for these results.
The fi rst four points have been plotted for you.
(b) What type of correlation does this scatter diagram show?
(c) On the grid, draw the line of best fit.
(d) Use your line of best fit to estimate the temperature at a height of 1400m.
Answer/Explanation
Answer:
(a) 4 points plotted correctly
(b) negative
(c) correct ruled line
(d) 22.4 – 22.8
Question
12 athletes took part in the 100 metres race.
11 of these athletes also took part in the long jump.
The times and distances, each measured correct to 3 signifi cant fi gures, for these athletes are shown in the
table.
(a) The scatter diagram shows the times and distances for athletes B to H.
(i) Plot the times and distances for athletes I, J, K and L.
Answer/Explanation
Ans:
(ii) On the scatter diagram, draw a line of best fi t.
Answer/Explanation
Ans:
(iii) Athlete A did not take part in the long jump.
Use your line of best fi t to estimate a long jump distance for athlete A.
Answer/Explanation
Ans:
(iv) What type of correlation is shown on the scatter diagram?
Answer/Explanation
Ans:
(v) Describe in words the relationship between the time for 100 metres and the distance in the long jump.
Answer/Explanation
Ans:
(b) Use the table of times and distances to work out
(i) the mean of the 100 metres times,
Answer/Explanation
Ans:
(ii) the percentage of athletes who ran 100 metres in less than 11.5 seconds,
Answer/Explanation
Ans:
(iii) the range of the distances jumped by the 11 athletes, B to L.
Answer/Explanation
Ans:
Question
(a) Ten students take a physics examination and a mathematics examination.
Their scores are recorded in the table below.
(i) Complete the scatter diagram.
The first six points have been plotted for you.
Answer/Explanation
Ans: 4 points correctly plotted
(ii) What type of correlation is shown by the scatter diagram?
Answer/Explanation
Ans: positive
(iii) On the grid, draw a line of best fit.
Answer/Explanation
Ans: correct ruled straight line
(iv) Another student scored 52 in the mathematics examination.
Use your line of best fit to estimate this student’s score in the physics examination.
Answer/Explanation
Ans: 74
(b) This graph can be used to convert between pounds (lb) and kilograms (kg).
Use the graph to convert
(i) 50 pounds to kilograms,
Answer/Explanation
Ans: 22 < Ans ≤ 23
(ii) 275 kilograms to pounds.
Answer/Explanation
Ans: 590 ≤ ans ≤ 620
Question
Ten students estimate the length and width of their rectangular school hall.
The results are shown in the table.
The first 8 results have been plotted on the scatter diagram.
(a) On the scatter diagram, plot the results for students I and J.
(b) What type of correlation is shown by this scatter diagram?
(c) (i) On the scatter diagram, draw a line of best fit.
(ii) Another student, Pedro, estimates the length of the hall as 31m.
His result for the width is missing.
Use your line of best fit to estimate his result for the width.
……………………….. m
(d) The actual measurements of the hall are length 44m and width 34m.
(i) The teacher says a ‘good estimator’ has both estimates no more than 5m from the actual
measurements.
Write down the letters of the students who are ‘good estimators’.
(ii) Work out the perimeter of the hall.
…………………… m
(iii) Calculate the length of a diagonal of the hall.
…………………………… m
(e) The hall is divided into two areas.
Find the shaded area.
………………………. \(m^2\)
Answer/Explanation
Answer:
(a) I, J correctly plotted
(b) positive
(c) (i) ruled line of best fit
(ii) 16 to 19
(d) (i) D,H, I
(ii) 156
(iii) 55.6 or 55.60 to 55.61
(e) 1020
Question
Lucy asked 12 people how many hours they each spent playing a computer game and the number of levels
they each completed in one month.
The results are shown in the table.
(a) Complete the scatter diagram.
The first eight points have been plotted for you.
(b) One person completes more levels per hour than any of the others.
On the scatter diagram, put a ring around the point for this person.
(c) What type of correlation does this scatter diagram show?
…………………………………………
(d) On the scatter diagram, draw a line of best fit.
(e) Another person, Monika, completed 19 levels but forgot to record the time spent playing.
Use your line of best fit to estimate the number of hours that Monika spent playing.
………………………………… hours
Answer/Explanation
(a) 4 points correctly plotted
(b) (40, 18) indicated
(c) Positive
(d) Correct ruled line
(e) 76 to 80
Question
Fourteen students each take two tests in French, a speaking test and a written test.
The table shows the scores.
(a) Complete the scatter diagram.
The first ten points have been plotted for you.[2]
(b) What type of correlation is shown in this scatter diagram?[1]
(c) One student has a high score in the speaking test and a low score in the written test.
On the scatter diagram, put a ring around this point. [1]
(d) On the scatter diagram, draw a line of best fit. [1]
(e) Use your line of best fit to estimate a score in the written test for a student who scored 25 in the speaking test.[1]
Answer/Explanation
Ans:
6(a) 4 points correctly plotted
6(b) Positive
6(c) (40, 20) indicated
6(d) Ruled line of best fit
6(e) 33 to 42