The observations 56, 58, 63, x-5, x+1, 75, 81 | vedclass

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(B) The given observations are $56, 58, 63, x-5, x+1, 75, 81, 85$. Total number of observations $n = 8$,which is an even number. For an even number of

Vedclass · Accepted Answer

$69$

Vedclass · Answer

(B) The given observations are $56, 58, 63, x-5, x+1, 75, 81, 85$. Total number of observations $n = 8$,which is an even number. For an even number of observations,the median is the average of the $(\frac{n}{2})^{th}$ and $(\frac{n}{2} + 1)^{th}$ terms. Here,$n = 8$,so the median is the average of the $4^{th}$ and $5^{th}$ terms. $4^{th}$ term $= x-5$ $5^{th}$ term $= x+1$ Median $= \frac{(x-5) + (x+1)}{2} = 67$ $\frac{2x - 4}{2} = 67$ $x - 2 = 67$ $x = 69$.

Mid-point	Frequency
$5$	$4$
$15$	$8$
$25$	$13$
$35$	$12$
$45$	$6$

$x$	$f$
$10$	$17$
$30$	$5a+3$
$50$	$32$
$70$	$7a-11$
$90$	$19$

Class	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$1$	$4$	$5$	$10$	$5$	$4$	$1$

The observations $56, 58, 63, x-5, x+1, 75, 81, 85$ have been arranged in ascending order. If the median of the data is $67$,find the value of $x$.

Similar Questions

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Mid-point Frequency

$5$ $4$

$15$ $8$

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Also,find the size of the class intervals.

The mean of the following distribution is $50$. Find the value of $a$ and hence the frequencies of $30$ and $70$.
$x$ $f$
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$30$ $5a+3$
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Find the mean,the median,and the mode of the observations:
$48, 41, 36, 35, 41, 37, 39, 52, 41, 48$

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