In a study on patients, the following data were obtained. Find the arithmetic mean.
Age (in yrs) $10 - 19$ $20 - 29$ $30 - 39$ $40 - 49$ $50 - 59$
No. of patients $1$ $0$ $1$ $10$ $13$

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Solution

Age

Midpoints

No.of patients

10-19

14.5

1

20-29

24.5

0

30-39

34.5

1

40-49

44.5

10

50-59

54.5

13

N=25

Mean $= \frac{14.5 \times 1 + 24.5 \times 0 + 34.5 \times 1 + 44.5 \times 10 + 54.5 \times 13}{25}$
Mean $= \frac{14.5 + 0 + 34.5 + 445 + 708.5}{25} = \frac{1202.5}{25} = 48.1$

Hence,average age= $48.1$ years

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No. of patients	7	19	11	9	1

Ages	10-20	20-30	30-40	40-50	50-60
No. of patients	7	11	19	9	1

Age in years	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
No. of patients	$2$	$5$	$12$	$19$	$9$	$3$

Age group	$0 - 9$	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 59$	$60 - 69$
No. of persons	$4$	$6$	$10$	$11$	$12$	$6$	$1$

150

Age (yrs)	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
No. of patients	$12$	$14$	$36$	$50$	$20$	$18$

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Age (in yrs)	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 59$
No. of patients	$1$	$0$	$1$	$10$	$13$