Question

6, 8, x + 2, 10, 2x - 1, and 2 is 9 is the mean what is the median

Answer 1

★ How to do :-

Here, we are given with a data in which we are given two of them in the form of a variable. We are also given with the mean value of the data. We are asked to find the median of the same data. So, first we should find the both not-given values of the data, which are given by the variable format. To find the value of the variable x, we use a concept called as transition of numbers and variables from one hand side to the other. By this, we find the value of all the observations of the data. Then, we arrange the observations in the form of ascending order and then, we can find the median. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \underline{\boxed{\sf Mean = \dfrac{Sum \: of \: all \: observations}{Number \: of \: observations}}}}$

Substitute the given values.

${\tt \leadsto 9 = \dfrac{6 + 8 + (x + 2) + 10 + (2x - 1) + 2}{6}}$

Add all the values in the numerator.

${\tt \leadsto 9 = \dfrac{26 + (x + 2) + (2x - 1)}{6}}$

Add the variables on the numerator.

${\tt \leadsto 9 = \dfrac{26 + 3x + 1}{6}}$

Shift the number 6 from RHS to LHS.

${\tt \leadsto 9 \times 6 = 26 + 3x + 1}$

Multiply the value on LHS and add the numbers on RHS.

${\tt \leadsto 54 = 27 + 3x}$

Shift the number 27 from RHS to LHS, changing it's sign.

${\tt \leadsto 54 - 27 = 3x}$

Subtract the values on LHS.

${\tt \leadsto 27 = 3x}$

Shift the number 3 from LHS to RHS.

${\tt \leadsto x = \dfrac{27}{3}}$

Simplify the fraction to get the value of x.

${\tt \leadsto x = 9}$

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Now, we should find the value of third and fourth observation.

Value of third observation :-

${\tt \leadsto x + 2}$

Substitute the value of x.

${\tt \leadsto 9 + 2}$

Add the values.

${\tt \leadsto 11}$

Value of fifth observation :-

${\tt \leadsto 2x - 1}$

Substitute the value of x.

${\tt \leadsto 2 (9) - 1}$

Multiply the numbers first.

${\tt \leadsto 18 - 1}$

Subtract the values.

${\tt \leadsto 17}$

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Now, let's find the ascending order of the given data.

Ascending order :-

⇝2, 6, 8, 10, 11, 17

Median :-

${\sf \leadsto \underline{\boxed{\sf Median = \dfrac{n}{2} + 1th \: \: term}}}$

Substitute the value of n.

${\tt \leadsto \dfrac{6}{2} + 1th \: \: term}$

Simplify the given fraction.

${\tt \leadsto 3 + 1th \: \: term}$

Add the values.

${\tt \leadsto 4th \: \: term}$

We can see that the fourth term is 10. So, the median is 10.

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${\red{\underline{\boxed{\bf So, \: the \: median \: of \: the \: data \: is \: \: 10.}}}}$