MATHEMATICS · Multi-part · A Level · Mathematics · Data presentation and interpretation · Data presentation and interpretation
Problem
For the two data sets given below, answer the following questions.
Data set P: 3, 4, 5, 6, 7
Data set Q: 1, 1, 5, 9, 9
(i) Define (a) range and (b) variance for an ungrouped data set.
(ii) Determine the range of each data set without showing intermediate working.
(iii) Explain, with two clear reasons, why the range calculated in part (ii) may not be sufficient to compare the overall spread of the two data sets.
(iv) State any two advantages of using variance (or standard deviation) over range for comparing the variability of P and Q.