Math, asked by khalidvahora25, 4 months ago

the following data have been arranged in ascending order:
18,20,25,26,30,x,37,38,39,48
if the median of the data is 35, find x. in the above data, if 48 is replaced by 28 ,find the new median

Answers

Answered by MasterDhruva
5

How to do :-

Here, we are given with some data with ten observations and the median of that data. In that, we are not given with one observation which is written as a variable. We are asked to find the value of 'x' in the first sub-question and in the second sub-question, we are given that the observation 48 is replaced with 28 in which we are asked to find the new median. So, first we should find the value of the variable and then we can find the new median. So, let's solve!!

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Solution (1) :-

Value of 'x' :-

{\tt \leadsto 18, 20, 25, 26, 30, x, 37, 38, 39, 48}

We know that the middle value, when arranged in ascending or descending order is the median of those observations. So,

{\tt \leadsto \cancel{18}, \cancel{20}, \cancel{25}, \cancel{26}, 30, x, \cancel{37}, \cancel{38}, \cancel{39}, \cancel{48}}

We have obtained with two numbers. So,

{\tt \leadsto \dfrac{30 + x}{2} = 35}

{\tt \leadsto 30 + x = 35 \times 2}

{\tt \leadsto 30 + x = 70}

{\tt \leadsto x = 70 - 30}

{\tt \leadsto \underline{\boxed{\tt x = 40}}}

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Solution (2) :-

{\tt \leadsto 18, 20, 25, 26, 28, 30,  37, 38, 39, 40}

{\tt \leadsto \cancel{18}, \cancel{20}, \cancel{25}, \cancel{26}, 28, 30, \cancel{37}, \cancel{38}, \cancel{39}, \cancel{40}}

Now,

Median :-

{\tt \leadsto \dfrac{28 + 30}{2} = \dfrac{58}{2}}

{\tt \leadsto \cancel \dfrac{58}{2} = \boxed{\tt 29}}

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Hence solved !!

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More to know :-

  • Mean is also known as Arthemetic mean. It is calculated by adding all the observations and then divide it by the number of observations. It's also known as average.

{\sf \longrightarrow Mean :- \: \dfrac{Sum \: of \: all \: observations}{Number \: of \: observations}}

  • Median is the middle number of the observations. First, we should arrange them in ascending or descending order. Then, we should find the middle value. If we obtain with two numbers, then we should find the mean of them.
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