Question

the following observations have been arranged in ascending order .If the median of data is 78 find the value of x. 44,47, 63,x+13,87,93,99,110
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Answer 1

Answer:

56

Explanation:

Short, brief showcase of median

x-1, x, x+1 : when there are odd number quantity

Median should be number in the middle.

x = mean(x-1, x+1)

• Mean of first and last place is middle place.

x-1, x, x+1, x+2 : even number quantity

mean(x, x+1)=mean(x-1, x+2)

Mean of first and last place is middle place, however, middle place never exists.

• We use two numbers that are close to the middle.

Solution : The median is mean of 4th and 5th data.

Mean of x+13 and 87 equals 78, which means x equals 56.

∵ $\frac{x+13+87}{2} =78$

$x+100=156$

∴ $x=56$

Answer 2

$\huge\mathbb{\underline{SOLUTION:-}}$

$\sf\underline{\purple{\:\:\:\: Given\:\:\:\:}}$

$\sf\bullet Median\:of\:data=78\\ \\ \sf\:\:\:\:\bullet\:\:Data\:is\\ \\ \sf\:\: 44,\:47,\:63,\:x+13,\:87\:,93\:,99\:,110$

Now we have to find the value of x in the given data

$\sf\bullet{\purple{Number\:of\: observation=8(even\: number)}}$

$\boxed{\sf{Median=\dfrac{\bigg(\dfrac{n}{2}\bigg){}^{th}\:term+\bigg (\dfrac{n}{2}+1 \bigg){}^{th}\:term}{2}}}$

Where n is the total number of observation

$\sf\underline{\red{\:\:\:\: Solution\:\:\:\:}}$

$\sf:\implies 78=\dfrac{\bigg(\dfrac{8}{2}\bigg){}^{th}term+\bigg(\dfrac{8}{2}+1\bigg){}^{th}\:term}{2}\\ \\ \sf:\implies 78=\dfrac{\bigg(\dfrac{8}{2}\bigg){}^{th}term+\bigg(\dfrac{10}{2}\bigg)th\:term}{2}\\ \\ \sf\implies78= \dfrac{4th\:term+5th\:term}{2}\\ \\ \sf\bullet 4th\:term=x+13\\ \\ \sf\bullet 5th\:term=87\\ \\ \sf:\implies 78=\dfrac{x+13+87}{2}\\ \\ \sf:\implies 78\times 2=x+100\\ \\ \sf:\implies 156=x+100\\ \\ \sf:\implies x=156-100\\ \\ \sf:\implies x=56$

The value of x is 56

So 4th observation=56+13= 69

$\huge\mathfrak{\pink{x=56}}$