A frequency distribution of the life times of $400$ T.V. picture tubes tested in a tube company is given. Find the average life time of a tube.
Life time (in hrs) Frequency Life time (in hrs) Frequency
$300 - 399$ $14$ $800 - 899$ $62$
$400 - 499$ $46$ $900 - 999$ $48$
$500 - 599$ $58$ $1000 - 1099$ $22$
$600 - 699$ $76$ $1100 - 1199$ $6$
$700 - 799$ $68$

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Solution

$L i f e t i m e$
$(i n h r s)$ $C l a s s - m a r k$
$x_{i}$ $F r e q u e n c y$
$f_{i}$ $f_{i} x_{i}$
$299.5 - 399.5$ $349.5$ $14$ $4893$
$399.5 - 499.5$ $449.5$ $46$ $20677$
$499.5 - 599.5$ $549.5$ $58$ $31871$
$599.5 - 699.5$ $649.5$ $76$ $49362$
$699.5 - 799.5$ $749.5$ $68$ $50966$
$799.5 - 899.5$ $849.5$ $62$ $52669$
$899.5 - 999.5$ $949.5$ $48$ $45576$
$999.5 - 1099.5$ $1049.5$ $22$ $23089$
$1099.5 - 1199.5$ $1149.5$ $6$ $6897$
$\sum f_{i} = 400$ $\sum f_{i} x_{i} = 286000$
$\Rightarrow$ $M e a n = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{286000}{400} = 715$

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Similar questions

Q. The table shows a frequency distribution of the life time of

400

radio tubes tested at a company.

Life time (hours)	Number of tubes	Life time (hours)	Number of tubes
$300 - 399$	$14$	$800 - 899$	$62$
$400 - 499$	$46$	$900 - 999$	$48$
$500 - 599$	$58$	$1000 - 1099$	$22$
$600 - 699$	$76$	$1100 - 1199$	$6$
$700 - 799$	$68$
			Total $400$

Column

I I

gives data for description given in column

I

, match them correctly.

Q. A frequency distribution of the of life times 400 T.V. picture tubes tested in a tube company is given below. Find the average life of tube.

Life time ( in hrs)	Frequency
300-399	14
400-499	46
500-599	58
600-699	76
700-68	68
800-899	62
900-999	48
1000-1099	22
1100-1199	6

The following table gives the life times of 400 neon lamps :

(i)

Represent the given information with the help of histogram.

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

(i i)

How many lamps have a life time more than

700

hours?

The following table gives the life time of 400 neon lamps:

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

A bulb is selected at random. Find the probability that the life time of the selected bulb is:

(i) less than 400 (ii) between 300 to 800 hours (iii) at least 700 hours.

Q. The following table gives the life time of 400 neon lamps:

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

A bulb is selected of random, Find the probability that the the life time of the selected bulb is:
(i) less than 400
(ii) between 300 to 800 hours
(iii) at least 700 hours.

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Life time (in hrs)	Frequency	Life time (in hrs)	Frequency
$300 - 399$	$14$	$800 - 899$	$62$
$400 - 499$	$46$	$900 - 999$	$48$
$500 - 599$	$58$	$1000 - 1099$	$22$
$600 - 699$	$76$	$1100 - 1199$	$6$
$700 - 799$	$68$

$L i f e t i m e$ $(i n h r s)$	$C l a s s - m a r k$ $x_{i}$	$F r e q u e n c y$ $f_{i}$	$f_{i} x_{i}$
$299.5 - 399.5$	$349.5$	$14$	$4893$
$399.5 - 499.5$	$449.5$	$46$	$20677$
$499.5 - 599.5$	$549.5$	$58$	$31871$
$599.5 - 699.5$	$649.5$	$76$	$49362$
$699.5 - 799.5$	$749.5$	$68$	$50966$
$799.5 - 899.5$	$849.5$	$62$	$52669$
$899.5 - 999.5$	$949.5$	$48$	$45576$
$999.5 - 1099.5$	$1049.5$	$22$	$23089$
$1099.5 - 1199.5$	$1149.5$	$6$	$6897$
		$\sum f_{i} = 400$	$\sum f_{i} x_{i} = 286000$

A frequency distribution of the life times of 400 T.V. picture tubes tested in a tube company is given. Find the average life time of a tube. Life time (in hrs)FrequencyLife time (in hrs)Frequency300−39914800−89962400−49946900−99948500−599581000−109922600−699761100−11996700−79968