I am one of those who keep trying to solve without a formula and lose on time.. so trying to strike a balance
aimtoteach wrote:
The original Median is 38 for this set of scores.
I did quick summations to reach at option B wherein the Median increases to 39 - for all others it remains at 38.
Is there another way to do it via a formula or something?
Cribbing for the formula where it's not needed is the first sign of going on wrong path of learning.So beware!
Statistics doesn't require any formula. It just requires basic understanding of Median, Standard Deviation, Mode (rarely) and Range.
basic conceptual method is right here
CONCEPT: Median is the middle terms (for odd no. of terms in set) or Average of two middle terms (for Even no. of terms in set) in the set after arranging the terms in Ascending/Descending order.
Here the Set (in Ascending order) is {15, 22, 38, 51, 63} i.e. Median = 38
Now, an integer number of Keri's points were taken from her and given to Luke, and the median score of the 5 players increased
Let's say x was the number of points transferred from Keri's points to Luke's points.
Now the Set becomes {15+x, 22, 38, 51, 63-x} But now the median becomes a bigger number
i.e. The New median could be either 51 or 63-x where both these numbers must be greater than 38
But, For Median = 51, 63-x and 15+x both should be greater than 51 Which is NOT POSSIBLE
Hence, Median Must be 63-x, and 15+x should be greater than 38
i.e. 38 < 63-x < 51 AND 15+x > 38
i.e. 12 < x < 25 AND x > 23
i.e. x can only be 24