plumiCorrelation and regression: OCR A‑Level Further Maths questions
Every OCR A-Level Further Maths exam question on FS.5 Correlation and regression, 2018–2025, with its mark scheme and examiner’s report.
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All 29 questions on Correlation and regression, as a list
- June 2025, Statistics, Q1 (4 marks): A set of 16 observations of the bivariate data (X, Y ) are summarised as follows. 2 2 n 16 x 136 y 352 x 1496 y 9104 xy 3642 / / / / / = = = = = = Determine an
- June 2025, Statistics, Q7 (9 marks): (a) A large number of competitors take part in two races. A random sample of 6 competitors who take part in both races is obtained. The value of Spearman’s rank
- June 2025, AS Statistics, Q3 (10 marks): (a) It is required to test whether there is a relationship between two numerical variables. State why in certain circumstances it would be better to use a test
- June 2025, AS Statistics, Q4 (11 marks): In a science experiment, the values of a variable W are selected by the scientist. The experiment involves measuring the corresponding values of the variable V.
- June 2024, Statistics, Q2 (9 marks): A newspaper article claimed that “taller dog owners have taller dogs as pets”. Alex investigated this claim and obtained data from a random sample of 16 fellow
- June 2024, Statistics, Q7 (8 marks): The coordinates of a set of 10 points are denoted by ( , x y i for i ) = , 2, …, 10. 1 i For a particular set of values of ( , x y i and any constants a and b i
- June 2024, AS Statistics, Q3 (11 marks): The ages, x years, and the reaction time, t seconds, in an experiment carried out on a sample of 15 volunteers are summarised as follows. 2 = 2 = n 15 x 762 t 8
- June 2024, AS Statistics, Q5 (9 marks): In a fashion competition, two judges gave marks to a large number of contestants. The value of Spearman’s rank correlation coefficient, rs, between the marks gi
- June 2023, Statistics, Q2 (8 marks): The director of a concert hall wishes to investigate if the price of the most expensive concert tickets affects attendance. The director collects data about the
- June 2023, Statistics, Q4 (10 marks): Two magazines give numerical ratings to hi-fi systems. Li wishes to test whether there is agreement between the opinions of the magazines. Li chooses a random s
- June 2023, AS Statistics, Q3 (8 marks): An insurance company collected data concerning the age, x years, of policy holders and the average size of claim, £y thousand. The data is summarised as follows
- June 2023, AS Statistics, Q5 (9 marks): A psychologist investigates the relationship between ‘openness’ and ‘creativity’ in adults. Each member of a random sample of 15 adults is given two tests, one
- June 2022, Statistics, Q2 (11 marks): The directors of a large company believe that there are more computer failures in the Head Office when temperatures are higher. They obtain data for the Head Of
- June 2022, AS Statistics, Q1 (8 marks): A geography student chose a certain point in a stream and took measurements of the speed of - , of water at various depths, d m, below the surface at that point
- June 2022, AS Statistics, Q2 (7 marks): Eight runners took part in two races. The positions in which the runners finished in the two races are shown in the table. Runner A B C D E F G H First race 3 1
- November 2021, Statistics, Q1 (6 marks): At a seaside resort the number X of ice-creams sold and the temperature Y °F were recorded on 20 randomly chosen summer days. The data can be summarised as foll
- November 2021, Statistics, Q5 (10 marks): The numbers of each of 9 items sold in two different supermarkets in a week are given in the following table. Item 1 2 3 4 5 6 7 8 9 Supermarket A 17 28 41 43 6
- November 2021, AS Statistics, Q2 (7 marks): A shopper estimates the cost, £X per item, of each of 12 items in a supermarket. The shopper’s estimates are compared with the actual cost, £Y per item, of each
- November 2021, AS Statistics, Q3 (7 marks): (a) Using the scatter diagram in the Printed Answer Booklet, explain what is meant by least squares in the context of a regression line of y on x. [2] (b) A set
- November 2020, Statistics, Q2 (8 marks): A book collector compared the prices of some books, £x, when new in 1972 and the prices of copies of the same books, £y, on a second-hand website in 2018. The r
- November 2020, AS Statistics, Q1 (5 marks): Five observations of bivariate data (x, y) are given in the table. x 7 8 12 6 4 y 20 16 7 17 23 (a) Find the value of Pearson’s product-moment correlation coeff
- November 2020, AS Statistics, Q3 (9 marks): An investor obtains data about the profits of 8 randomly chosen investment accounts over two one-year periods. The profit in the first year for each account is
- November 2020, AS Statistics, Q4 (9 marks): After a holiday organised for a group, the company organising the holiday obtained scores out of 10 for six different aspects of the holiday. The company obtain
- June 2019, Statistics, Q1 (5 marks): A set of bivariate data (X, Y ) is summarised as follows. n 25 , x 9 975 . , y 11 175 . , x 2 5 725 . , y 2 46 200 . , xy 11 575 . / / / / / = = = = = = (a) Cal
- June 2019, Statistics, Q5 (7 marks): Five runners, A, B, C, D and E, take part in two different races. Spearman’s rank correlation coefficient for the orders in which the runners finish is calculat
- June 2019, AS Statistics, Q3 (6 marks): (a) Shula calculates the value of Spearman’s rank correlation coefficient rs for 9 pairs of rankings. Find the largest possible value of rs that Shula can obtai
- June 2019, AS Statistics, Q5 (7 marks): Sixteen candidates took an examination paper in mechanics and an examination paper in statistics. (a) For all sixteen candidates, the value of the product momen
- June 2018, AS Statistics, Q4 (8 marks): Judith believes that mathematical ability and chess-playing ability are related. She asks 20 randomly chosen chess players, with known British Chess Federation
- June 2018, AS Statistics, Q7 (8 marks): An environmentalist measures the mean concentration, c milligrams per litre, of a particular chemical in a group of rivers, and the mean mass, m pounds, of fish
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