The table shows the frequency distribution of the ages of patients in a clinic. Ages…

The table shows the frequency distribution of the ages of patients in a clinic.

Ages (years)	17 – 19	20 – 22	23 – 28	29 – 34	35 – 43
No. of patients	6	9	12	18	18

(a) Draw a histogram for the distribution

(b) Find, correct to two decimal places, the mean age of the patients.

 

Explanation

Age (yr)	Frequency	Class boundary	Class width	Height
17 – 19	6	16.5 – 19.5	3	2
20 – 22	9	19.5 – 22.5	3	3
23 – 28	12	22.5 – 28.5	6	2
29 – 34	18	28.5 – 34.5	6	3
35 – 43	18	34.5 – 43.5	9	2

(a) 

(b) Let the assumed mean be 25.5 yrs.

Age (yr)	Mid-age (x)	Freq (f)	(d = x – A)	(fd)
17 – 19	18	6	-7.5	-45
20 – 22	21	9	-4.5	-40.5
23 – 28	25.5	12	0	0
29 – 34	31.5	18	6.0	108
35 – 43	39.0	18	13.5	243
		63		265.5

Mean = (A + frac{sum fd}{sum f})

= (25.5 + frac{265.5}{63})

= (25.5 + 4.21)

= (29.71 yrs)