Question

Median of a data, arranged in ascending order 7, 10, 15, x. y, 27, 30 is 17 and when one more observation 50 is added to the data, the median has become 18 Find x andy ​

Answer 1

Step 1: Find the median of the given dates after arranging them in ascending order.

               We have, 7, 10, 15, x, y, 27, 30

               So, there are seven terms. that is n = 7

               ∴ Median = x                                                 [ ∵ $$\textbf{Median is $\bigg(\dfrac{n+1}{2}\bigg)^{th}$observation if n is odd.]}$$

               ⇒x=17                                                                                           ....(1)

               Again, 50 is added to the data.

               ∴ New data is 7, 10, 15, x, y, 27, 30, 50

               So, there are eight terms. that is n = 8

               ∴ Median =  

2

x+y

​

                 $$\textbf{ $\bigg[$$\because$$ \textbf{Median is }\dfrac{\bigg(\dfrac{n}{2}\bigg)^{\textbf{th}}+\bigg(\dfrac{n}{2}+1\bigg)^{\textbf{th}}\textbf{observation}}{2}$ if n is even}\bigg]$$

               ⇒

2

x+y

​

=18

               Cross-multiply,

                x + y = 36                                                                                       ....(2)

Step 2: Use the above results and evaluate unknown.

               ∴ From (2),

               17 + y = 36                                                                                 [Using (1)]

               ⇒y=19

Hence, answer is x = 17 and y = 19.