The table shows the frequency distribution of…

Question 1 Report

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.

Answer

Answer Details

(a) Histogram

Since the class intervals have unequal widths, plot frequency density against age.

Age class (years)	Class boundaries	Class width	Frequency	Frequency density \(=\frac{f}{\text{class width}}\)
17 - 19	16.5 - 19.5	3	6	2
20 - 22	19.5 - 22.5	3	9	3
23 - 28	22.5 - 28.5	6	12	2
29 - 34	28.5 - 34.5	6	18	3
35 - 43	34.5 - 43.5	9	18	2

(b) Mean age

Age class	Midpoint, \(x\)	Frequency, \(f\)	\(fx\)
17 - 19	18.0	6	108
20 - 22	21.0	9	189
23 - 28	25.5	12	306
29 - 34	31.5	18	567
35 - 43	39.0	18	702
Total		63	1872

\[\bar{x}=\frac{\sum fx}{\sum f}=\frac{1872}{63}=29.714\ldots\]

Therefore, the mean age of the patients is \(29.71\text{ years}\), correct to two decimal places.

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 ...