The scores

The scores of 10 learners in a test arranged in ascending order are 12, 13, 13, a, (a + 3), (52 - 2a), (2a - 8), 23, 23, and 24. If the median mark is 20, find (a) value of a. (b) mean

Final Answer:

a =  15
μ =  18.5

Step-by-step explanation:

n=10 m=20  m = 2a5​+a6​​  m = 2(a+3)+(52−2a)​  2⋅ m=(a+3)+(52−2a) 2⋅ 20=(a+3)+(52−2a)  2⋅ 20=(a+3)+(52−2⋅ a)  a=15
a5​=a+3=15+3=18 a6​=52−2⋅ a=52−2⋅ 15=22 a7​=2⋅ a−8=2⋅ 15−8=22  s=12+13+13+a+a5​+a6​+a7​+23+23+24=12+13+13+15+18+22+22+23+23+24=185  μ=ns​=10185​=237​=1821​=18.5

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