Statistics opens Paper 2 and carries about 20 marks. These are some of the most reliable marks in the exam if you know how to use your calculator and can explain what the numbers mean.
Question 1: Mean and standard deviation
Find the mean and standard deviation of 4; 7; 8; 10; 11. The mean is 40 ÷ 5 = 8. The squared deviations are 16, 1, 0, 4 and 9, which add to 30. The variance is 30 ÷ 5 = 6. Answer: mean = 8 and σ = √6 ≈ 2.45.
Question 2: Within one standard deviation
Using question 1, how many values lie within one standard deviation of the mean? The interval is 8 − 2.45 to 8 + 2.45, which is 5.55 to 10.45. The values 7, 8 and 10 lie inside it. Answer: 3 of the 5 values.
Question 3: Five-number summary
Give the five-number summary of 3; 5; 7; 8; 10; 12; 15. Answer: minimum 3, Q1 = 5, median 8, Q3 = 12, maximum 15.
Question 4: Interquartile range
Find the interquartile range for question 3. IQR = Q3 − Q1 = 12 − 5. Answer: 7.
Question 5: Skewness
A data set has a mean of 62 and a median of 55. Describe its shape. The mean is greater than the median, so the data is pulled towards higher values. Answer: positively skewed.
Question 6: Regression line
The least squares regression line is ŷ = 2.5 + 1.2x. Predict y when x = 10. ŷ = 2.5 + 1.2(10). Answer: 14.5. If x = 10 is outside the data range, say that the prediction is less reliable.
Question 7: Correlation
A data set has a correlation coefficient of r = 0.92. Describe the relationship between x and y. The value is positive and close to 1, so y tends to increase as x increases, and the points lie close to the regression line. Answer: a very strong positive correlation.
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