Find the arithmetic mean for the following grouped frequency distribution:
Class-intervals
$6 - 10$
$10 - 14$
$14 - 18$
$18 - 22$
$22 - 26$
$26 - 30$
Frequency
$4$
$6$
$9$
$12$
$7$
$2$

15.8

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16.8

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17.8

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None of these

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Solution

The correct option is C $17.8$
Consider the following table, to calculate mean:
$c i$ $f_{i}$ $x_{i}$ $f_{i} x_{i}$
$6 - 10$ $4$ $8$ $32$
$10 - 14$ $6$ $12$ $72$
$14 - 18$ $9$ $16$ $144$
$18 - 22$ $12$ $20$ $240$
$22 - 26$ $7$ $24$ $168$
$26 - 30$ $2$ $28$ $56$
From the table,
$N = Σ f_{i} = 4 + 6 + 9 + 12 + 7 + 2 = 40$

$Σ f_{i} x_{i} = 32 + 72 + 144 + 240 + 168 + 56 = 712$

Mean $¯ ¯ ¯ x = \frac{Σ f_{i} x_{i}}{N}$
$∴ ¯ ¯ ¯ x = \frac{712}{40} = 17.8$
Hence, option $C$ is correct.

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Class interval	10-14	14-18	18-22	22-26	26-30	30-34	34-38	38-42
Frequency	8	6	11	20	25	22	10	4

Class-interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Frequency	$7$	$14$	$28$	$26$	$16$	$9$

Class interval	10-14	14-18	18-22	22-26	26-30
Frequency	5	11	16	25	19

6, 8, 9, 12, 14, 18, 22, 26, 30

Class Interval	$0 - 9$	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 50$	$60 - 60$
Frequency	$8$	$10$	$22$	$26$	$18$	$9$	$7$

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Class-intervals	$6 - 10$	$10 - 14$	$14 - 18$	$18 - 22$	$22 - 26$	$26 - 30$
Frequency	$4$	$6$	$9$	$12$	$7$	$2$