Question

THE MEDIAN OF 9 DISTINCT OBSERVATIONS IS 20. IF EACH OF THE LARGEST 4 OBSERVATIONS OF THE SET IS INCREASED BY 2, FIND THE MEDIAN OF THE RESULTING SET

Answer 1

Answer:

Answer Expert Verified

Median of 9 observations = 9+1/2 th term = 5th term. The last term or the largest four are increased by 2 . But the fifth term is unchanged. The median of resultant set is same as the earlier.

Answer 2

Answer :-

If number of observations is odd, then

$\sf Median = Value \:of \: \Big(\dfrac{n+1}{2}\Big)^{th} \: observation$

Median for 9 observation =

$\implies\sf Value \:of \: \Big(\dfrac{9+1}{2}\Big)^{th} \: observation$

$\implies\sf\dfrac{5th \:observation}{2}$

Now, as the median is arranged in ascending order, largest four observation will be the last 4 observations i.e. 6th , 7th , 8th and 9th.

So, 6th , 7th , 8th and 9th are increased by 2. Here there is no effect on 5th term and the 5th observation is left unchanged. So there will be no effect on the median.

Resulting median will be left unchanged.