Calculate the mean life time of a bulb by step deviation
Life time (in hours)
400-499
500-599
600-699
700-799
800-899
900-999
No. of bulbs
24
47
39
42
34
14

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Solution

Life time (in hours)
No. of bulbs
$f i$
Mid values
$x i$
Deviation
$d i = x i - 750$
$U i = \frac{d i}{100}$ $f i U i$
$400 - 499$ $24$ $450$ $- 300$ $- 3$ $- 72$
$500 - 599$ $47$ $550$ $- 200$ $- 2$ $- 94$
$600 - 677$ $39$ $650$ $- 100$ $- 1$ $- 39$
$700 - 799$ $42$ $750$ $0$ $0$ $0$
$800 - 899$ $34$ $850$ $100$ $1$ $34$
$900 - 999$ $14$ $950$ $200$ $2$ $28$

$¯ x = A + h [\frac{1}{N} \sum f i U i]$
$¯ x = 750 + 100 [\frac{1}{200} (- 143)]$
$= 750 - 71.5$
$¯ x = 678.5$
The mean is $678.5$ hours.
$N = 200$ $- 143$

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Life time (in hours)	400-499	500-599	600-699	700-799	800-899	900-999
No. of bulbs	24	47	39	42	34	14

Life time (in hours)	No. of bulbs $f i$	Mid values $x i$	Deviation $d i = x i - 750$	$U i = \frac{d i}{100}$	$f i U i$
$400 - 499$	$24$	$450$	$- 300$	$- 3$	$- 72$
$500 - 599$	$47$	$550$	$- 200$	$- 2$	$- 94$
$600 - 677$	$39$	$650$	$- 100$	$- 1$	$- 39$
$700 - 799$	$42$	$750$	$0$	$0$	$0$
$800 - 899$	$34$	$850$	$100$	$1$	$34$
$900 - 999$	$14$	$950$	$200$	$2$	$28$
$¯ x = A + h [\frac{1}{N} \sum f i U i]$ $¯ x = 750 + 100 [\frac{1}{200} (- 143)]$ $= 750 - 71.5$ $¯ x = 678.5$ The mean is $678.5$ hours.	$N = 200$				$- 143$

Calculate the mean life time of a bulb by step deviationLife time (in hours)400-499500-599600-699700-799800-899900-999No. of bulbs244739423414

Calculate the mean life time of a bulb by step deviation
Life time (in hours)
400-499
500-599
600-699
700-799
800-899
900-999
No. of bulbs
24
47
39
42
34
14