(i) Write down the mean score in Round 1.

(ii) Write down the standard deviation in Round 1.

(iii) Find the number of these golfers that had a score of more than one standard deviation above the mean in Round 1.

Write down the correlation coefficient, r.

Write down the equation of the regression line of y on x.

Another golfer scored 70 in Round 1.

Calculate an estimate of his score in Round 2.

Another golfer scored 89 in Round 1.

Determine whether you can use the equation of the regression line to estimate his score in Round 2. Give a reason for your answer.

(i) \(\frac{{71 + 79 + ...}}{{12}}\)     (M1)

\(72.4\left( {72.4166...,{\text{ }}\frac{{869}}{{12}}} \right)\)     (A1)(G2)

Note: Award (M1) for correct substitution into the mean formula.

(ii) 4.77 (4.76896…)     (G1)

(iii) 72.4 + 4.77 = 77.17     (M1)

Note: Award (M1) for adding their mean to their standard deviation.

Two golfers     (A1)(ft)(G2)

Note: Follow through from their answers to parts (i) and (ii).

[5 marks]

0.990 (0.99014…)     (G2)

[2 marks]

y = 1.01x + 0.816 (y = 1.01404...x + 0.81618...)     (G1)(G1)

Notes: Award (G1) for 1.01x and (G1) for 0.816. If the answer is not an equation award a maximum of (G1)(G0).

OR

y − 74.25 = 1.01(x − 72.4)(y − 74.25 = 1.01404...(x − 72.4166...))     (A1)(A1)

Notes: Award (A1) for 1.01 correctly substituted in the equation, and (A1)(ft) for correct substitution of (72.4, 74.25) in the equation. Follow through from their part (a)(i). If the final answer is not an equation award a maximum of (A1)(A0).

[2 marks]

y = 1.01404... × 70 + 0.81618...     (M1)

Note: Award (M1) for substitution of 70 into their regression line equation from part (c).

y = 72 (71.7989...)     (A1)(ft)(G2)

Note: Follow through from their part (c).

[2 marks]

No, equation cannot be (reliably) used as 89 is outside the data range.     (A1)(R1)

OR

Yes, but the result is not valid/not reliable as 89 is outside the data range/as we extrapolate     (A1)(R1)

Note: Do not award (A1)(R0).

[2 marks]

The question was for the most part approached by almost all candidates and answered relatively well. The question in part (e) related to the use of the equation of the regression line for predicting, although regularly asked on exams, was still found to be a difficult one by some candidates. Some answers still suggested mathematical thinking and language unaccustomed to drawing conclusions and providing justifications.

The question was for the most part approached by almost all candidates and answered relatively well. The question in part (e) related to the use of the equation of the regression line for predicting, although regularly asked on exams, was still found to be a difficult one by some candidates. Some answers still suggested mathematical thinking and language unaccustomed to drawing conclusions and providing justifications.

The question was for the most part approached by almost all candidates and answered relatively well. The question in part (e) related to the use of the equation of the regression line for predicting, although regularly asked on exams, was still found to be a difficult one by some candidates. Some answers still suggested mathematical thinking and language unaccustomed to drawing conclusions and providing justifications.

The question was for the most part approached by almost all candidates and answered relatively well. The question in part (e) related to the use of the equation of the regression line for predicting, although regularly asked on exams, was still found to be a difficult one by some candidates. Some answers still suggested mathematical thinking and language unaccustomed to drawing conclusions and providing justifications.

The question was for the most part approached by almost all candidates and answered relatively well. The question in part (e) related to the use of the equation of the regression line for predicting, although regularly asked on exams, was still found to be a difficult one by some candidates. Some answers still suggested mathematical thinking and language unaccustomed to drawing conclusions and providing justifications.