Mathematics Theory The table shows the age distributions of the members of a club. Age (years) 10-14…

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?

 

 

Explanation

(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}).