Find the mean of the following distribution
300-400 400-500 500-600 600-700 700-800 800-900
No. of girls 4 18 9 7 6 3

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Solution

$C l a s s - i n t e r v a l$ $C l a s s - m a r k$
$x_{i}$ $f_{i}$ $f_{i} x_{i}$
$300 - 400$ $350$ $4$ $1400$
$400 - 500$ $450$ $18$ $8100$
$500 - 600$ $550$ $9$ $4950$
$600 - 700$ $650$ $7$ $4550$
$700 - 800$ $750$ $6$ $4500$
$800 - 900$ $850$ $3$ $2550$
$\sum f_{i} = 47$ $\sum f_{i} x_{i} = 26050$
$M e a n = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{26050}{47} = 554.26$

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C.I	0-100	100-200	200-300	30-400	400-500	500-600	600-700
F	10	15	25	25	10	10	5

CI	0-100	100-200	200-300	300-400	400-500	500-600	600-700	700-800	800-900	900-1000
Fr	2	5	x	12	17	20	y	9	7	4

Life time (in hours)	300-400	400-500	500-600	600-700	700-800	800-900	900-1000
Number of lamps:	14	56	60	86	74	62	48

\begin{matrix} Lifetime & 300 - 400 & 400 - 500 & 500 - 600 & 600 - 700 & 700 - 800 & 800 - 900 & 900 - 1000 (in hr) Number & 14 & 56 & 60 & 86 & 74 & 62 & 48 of lamps \end{matrix}

Electricity bill in a month (in Rs.)	200 - 400	400 - 600	600 - 800	800 - 1000
No. of families	362	490	185	63

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