Dynamics and StatisticsMedium
Question
Suppose that the mean and median of the nonnegative numbers 21, 8, 17, a, $51,103,\text{ }b,13,67$, $(a > b)$, are 40 and 21, respectively. If the mean deviation about the median is 26 , then 2 a is equal to :
Options
A.109
B.117
C.161
D.131
Solution
Sol. [Key Concept: Use mean $= 40$ and mean-deviation-about-median $= 26$ to get $a + b$ and $a - b$.]
8, 13, b, 17, 21, 51, a, 67, 103
$$\begin{matrix} mean = 40 = \frac{280 + a + b}{9} \\ a + b = 80 \end{matrix}$$
mean deviation about median
$$= \frac{13 + 8 + 4 + 30 + 46 + 82 + (a - 21) + (21 - b)}{9} = 26$$
$$a - b = 51$$
$$\Rightarrow 2a = 131 $$
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