1. GSCE Mathematics
Problem Solving
Handling Data
Higher Tier

2. 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

3. (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?

4. 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

5. 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

6. (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.

7. 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