Question

If the median of x + 2, x + 4, x + 6 ,x + 8 is 24 find x.

Answer 1

2x+10÷2=24

x+5=24

x=9

hope you get the step which is the mean of meddle numbers

Answer 2

$\huge{\bold{Answer:}}$

$\bf Step-by-step \: explanation:$

$\sf \underline{Given \: observations :-}$

x + 2, x + 4, x + 6, x + 8

No of observations, n = 4 (even)

Median = mean of $\mathsf{( \frac{n}{2} )\th}$ and $\mathsf{( \frac{n}{2} + 1 )\th}$ observations.

Median = mean of $\mathsf{( \frac{4}{2} )\th}$ and $\mathsf{( \frac{4}{2} + 1 )\th}$

Median = mean of 3rd and 4th observations.

Median = $\sf \frac{1}{2} * (x + 4 + x + 6)$

⇒ 24 = $\sf \frac{2x + 10}{2}$

⇒ 24 * 2 = 2 ( x + 5)

⇒ x + 5 = 24

⇒ x = 24 - 5

⇒ x = 19

$\underline{\bf{Hence,\: the \: value \: of \: x \: is \: 19.}}$

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$\huge{\bold{\underline{Extra \: information :}}}$

$\bf What \: is \: Median?$

After arranging the given data in the ascending or descending order of magnitude, the value of the middle most observation, is called the median of the data.

Formula to find the median :)

Method : Arrange the data in increasing or decreasing order of magnitude. Let the total number of observation be n.

(i) If n is odd, then median

⇒ Value of $\mathsf{( \frac{n + 1}{2} )\th}$ observation.

(ii) If n is even, then median

⇒ mean of $\mathsf{( \frac{n}{2} )\th}$ and $\mathsf{( \frac{n}{2} + 1 )\th}$ observations.

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