Compute the arithmetic mean of the following distribution.
Class Interval $0 - 19$ $20 - 39$ $40 - 59$ $60 - 79$ $80 - 99$
Frequency $3$ $4$ $15$ $14$ $4$

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Solution

Class Interval

MidPoint ( $x_{i}$ )

Frequency ( $f_{i}$ )

0-19

9.5

3

20-39

29.5

4

40-59

49.5

15

60-79

69.5

14

80-99

89.5

4

$\sum f_{i} = 40$

Mean $= \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{3 \times 9.5 + 4 \times 29.5 + 15 \times 49.5 + 14 \times 69.5 + 4 \times 89.5}{40} = 55.5$

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Class interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$
Frequency	$4$	$15$	$23$	$12$	$16$	$8$	$2$

Class interval	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 59$	$60 - 69$	$70 - 79$
Frequency	$6$	$4$	$10$	$9$	$11$	$8$	$2$

Class Intervals	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$
Frequency	$8$	$10$	$12$	$15$

=

$C I$	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 59$	$60 - 69$	$70 - 79$	$80 - 90$
$f$	$3$	$7$	$5$	$11$	$6$	$8$	$4$	$5$

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Class Interval	$0 - 19$	$20 - 39$	$40 - 59$	$60 - 79$	$80 - 99$
Frequency	$3$	$4$	$15$	$14$	$4$