The table shows the age distributions of the members of a club.
Age (years)
10-14
15-19
20-24
25-29
30-34
35-39
Frequency
7
18
25
17
9
4
(a) Calculate, correct to one decimal place, the mean age.
(b) (i) Draw a histogram to illustrate the information.
(ii) Use the histogram to estimate the modal age .
(c) If a member is selected at random, what is the probability that he/she is in the modal class?
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
Class Interval
Freq (f)
Classmark (x)
\(fx\)
10 - 14
7
12
84
15 - 19
18
17
306
20 - 24
25
22
550
25 - 29
17
27
459
30 - 34
9
32
288
35 - 39
4
37
148
80
1835
\(\bar{x} = \frac{\sum fx}{\sum f}\)
= \(\frac{1835}{80}\)
\(\approxeq 22.9yrs\)
(b)(i)
Class Interval
Freq (f)
Class boundaries
10 - 14
7
9.5 - 14.5
15 - 19
18
14.5 - 19.5
20 - 24
25
19.5 - 24.5
25 - 29
17
24.5 - 29.5
30 - 34
9
29.5 - 34.5
35 - 39
4
34.5 - 39.5
(ii) Modal age = \(\frac{20 + 24}{2} = 22\)
(c) P(picking from the modal class) = \(\frac{25}{80}\)
= \(\frac{5}{16}\).
Source: Myschool Past Questions Archive (Record #53118)