GSCE Mathematics Problem Solving Handling Data Higher Tier

Erin carried out a survey to find the age, in completed years, at which people marry. The table summarises the results for the women in the survey. The cumulative frequency diagram summarises the results for the men. Women Age (Completed Years) Youngest 18 Lower Quartile 26 Median 32 Upper Quartile 39 Oldest 57

(a) Erin decides to interview two people from her survey. She chooses one woman and one man at random. What is the probability that both the woman and the man are aged 32 or more when they get married? Helping hand Find the number of men getting married who are at least 32 years old. Use the table provided for women – the median is 32. How does this help you?

Answer Find the number of men getting married who are at least 32 years old. 35 people are less than 32, so 100 – 35 = 65 65 people are at least 32 years old

Answer The median is halfway i.e 50% of values are at least this value. So, P(woman at least 32) = 0.5 Women Age (Completed Years) Youngest 18 Lower Quartile 26 Median 32 Upper Quartile 39 Oldest 57 We also know that 65 out of 100 men are at least 32. So, P(man ≥ 32) = 0.65 P(Man AND Woman are at least 32) = P(Man ≥ 32) x P(Woman ≥ 32) = 0.65 x 0.5 = 0.325

(b) In her findings, Erin reported that ‘The range of the ages of men marrying was 43 and the oldest man to marry was 79’ Could this be true? Explain your answer. Helping hand Use the cumulative frequency diagram to help you. Look carefully at the intervals used.

Answer There are 1 or 2 men in the 60-80 category In her findings, Erin reported that ‘The range of the ages of men marrying was 43 and the oldest man to marry was 79’ Could this be true? Explain your answer. It is possible for the oldest man to be 79, however, if the range was also 43, this would make the youngest man: 79 – 43 = 36 We can see from the diagram that there were men who were less than 30, so this statement cannot be true. There are about 26 men who are less than 30 years old