GSCE Mathematics

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?
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.

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