Handling Data 4
5 marks · HardA club has 80 members. The table summarizes the ages of its members:
| Age (years) | Number of members |
|---|---|
| 10–19 | 23 |
| 20–34 | 18 |
| 35–49 | 25 |
| 50–64 | 9 |
| 65–80 | 5 |
The mid-interval values for the age groups are: 14.5, 27, 42, 57, and 72.5 respectively.
Estimate the mean age of the members. Give your answer to 1 decimal place.
A member is chosen at random. Estimate the probability that this member is younger than 35 years old.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 31.6 years
(b) 0.5125
Common mistakes: using endpoints instead of mid-interval values; not dividing by total members
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Multiply each number of members by the corresponding mid-interval value and sum.
M2 (a) · 1 mark · Divide the total sum by the total number of members (80). (follow-through)
A1 (a) · 1 mark · Correct answer for mean to 1 decimal place. (follow-through)
M3 (b) · 1 mark · Add the frequencies for the groups less than 35 and divide by 80.
A2 (b) · 1 mark · Correct probability, given to 3 significant figures (within tolerance). (follow-through)
Worked solution
To estimate the mean:
Mean = 34.3 (to 1 d.p.).
Probability (member under 35) = (23 + 18) / 80 = 41 / 80 = 0.5125.