If the median of learners is 20 then the value of a is 15 and the mean is 18.5.
Given that the scores of 10 learners in a test arranged in ascending order be 12, 13, 13, a, (a + 3), (52-2a), (2a-8), 23, 23 and 24 and the median mark is 20.
We are required to find the value of a and the value of mean.
Because n is odd so the median value will be the average of n/2 th term and (n+1)/2 th term.
(n/2)=10/2=5th term=a+3
(n/2)+1=10/2+1=5+1=6th term=52-2a
Median=(a+3+52-2a)/2
Median=(55-a)/2
20=(55-a)/2
40=55-a
a=55-40
a=15
Mean=(12+13+13+a+a+3+52-2a+2a-8+23+23+24)/10
=(155+2a)/10
=(155+2*15)/10
=(155+30)/10
=185/10
=18.5
Hence if the median of learners is 20 then the value of a is 15 and the mean is 18.5.
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