Question

Find the value of X if median of the data is 13 and is arranged in ascending order. 3,7,8,x+1,x+3,12,15,18

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Answer 1

The value of x is 11.

Step-by-step explanation:

We are given the median of the following data arranged in ascending order below;

 3, 7, 8, x+1, x+3, 12, 15, 18

For calculating median, firstly we have to check that the number of observations (n) in the data is even or odd;

• If n is odd, then the formula for calculating median is given by;

                  Median  =  $(\frac{n+1}{2} )^{th}$ observation

• If n is even, then the formula for calculating median is given by;

                  Median  =  $\frac{(\frac{n}{2})^{th}obs.+(\frac{n}{2}+1)^{th}obs. }{2}$

Now, here in our data the number of observation is even, i.e. n = 8.

SO,  Median  =  $\frac{(\frac{n}{2})^{th}obs.+(\frac{n}{2}+1)^{th}obs. }{2}$

              13     =  $\frac{(\frac{8}{2})^{th}obs.+(\frac{8}{2}+1)^{th}obs. }{2}$

              13     =  $\frac{4^{th}obs.+5^{th}obs. }{2}$

              13     =  $\frac{(x+1)+(x+3)}{2}$

              13     =  $\frac{2x+4}{2}$

              $2x+4 = 13 \times 2$

               $2x=26-4$

                $2x=22$

                 x = $\frac{22}{2}=11$

Therefore, the value of x in the data is 11.