Question

find the value of x The median of the given data 6,8,9,15,x,x+1,21,22,25,29,is 17.5​

Answer 1

Given :

• Observations - 6, 8, 9, 15, x, x+1, 21, 22, 25, 29.
• Median = 17.5

To Find :

The value of x.

Solution :

Here we first have to check whether the no of observations is even or odd. According to that information we can find the value of x using median.

Explanation :

6, 8, 9, 15, x, x+1, 21, 22, 25, 29.

• n = 10 (even)

So, the formula of median for even no of observations,

$\\ \bf Median=\dfrac{\left(\dfrac{n}{2}\right)^{th\ observation}+\left(\dfrac{n}{2}+1\right)^{th\ observation}}{2}$

where,

• n = 10

Substituting the values,

$\\ :\implies\sf Median=\dfrac{\left(\dfrac{10}{2}\right)^{th\ observation}+\left(\dfrac{10}{2}+1\right)^{th\ observation}}{2}$

$\\ :\implies\sf Median=\dfrac{\left(\dfrac{\cancel{10}}{\not{2}}\right)^{th\ observation}+\left(\dfrac{\cancel{10}}{\not{2}}+1\right)^{th\ observation}}{2}$

$\\ :\implies\sf Median=\dfrac{\left(5\right)^{th\ observation}+\left(5+1\right)^{th\ observation}}{2}$

$\\ :\implies\sf Median=\dfrac{\left(5\right)^{th\ observation}+\left(6\right)^{th\ observation}}{2}$

Now,

ATQ,

$\bf Median=\dfrac{\left(5\right)^{th\ observation}+\left(6\right)^{th\ observation}}{2}$

where,

• Median = 17.5
• 5th observation = x
• 6th observation = x + 1

Substituting the values,

$\\ :\implies\sf 17.5=\dfrac{x+x+1}{2}$

$\\ :\implies\sf 17.5\times2=2x+1$

$\\ :\implies\sf 35=2x+1$

$\\ :\implies\sf 35-1=2x$

$\\ :\implies\sf 34=2x$

$\\ :\implies\sf \dfrac{34}{2}=x$

$\\ :\implies\sf \cancel{\dfrac{34}{2}}=x$

$\\ :\implies\sf 17=x$

$\\ \therefore\boxed{\bf x=17.}$

The value of x is 17.

Explore More :

Median for odd observations,

$\bf Median=\left(\dfrac{n+1}{2}\right)th\ observation$

where,

• n = odd no of observations