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 that data , the median has become 18. Find x and y.

Answer 1

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Answer 2

Answer:

The value of x is 17 and the value of y is 19.

Step-by-step explanation:

The given observations are

$7,10,15,x,y,27,30$

Total number of observations is 7, which is an odd number. So the median of the data is

$M=\frac{n+1}{2}\text{ th term}$

$M=\frac{7+1}{2}\text{ th term}$

$M=\frac{8}{2}\text{ th term}$

$M=4\text{ th term}$

Fourth term of the data is x and the median of the data is 17.

$17=x$

Therefore the value of x is 17.

One more observation 50 is added to that data, now the data is

$7,10,15,x,y,27,30,50$

Total number of observations is 8, which is an even number. So the median of the data is

$M=\frac{\frac{n}{2}\text{ th term}+(\frac{n}{2}+1)\text{ th term}}{2}$

$M=\frac{\frac{8}{2}\text{ th term}+(\frac{8}{2}+1)\text{ th term}}{2}$

$M=\frac{4\text{ th term}+5\text{ th term}}{2}$

$M=\frac{x+y}{2}$

Now the median of the data is 18 and the value of x is 17.

$18=\frac{17+y}{2}$

$36=17+y$

$19=y$

Therefore, the value of x is 17 and the value of y is 19.