find 3 numbers that have the MAD= 1 (mean absolute deviation)
The Mean Absolute Deviation (MAD) of a data set is the average distance between each data value and the mean of the data set.
Let a,b,c be 3real numbers. Then their mean is (a+b+c)/3. The mean absolute distance of a from the mean is |a-(a+b+c)/3| = |(2a-b-c)/3|. Similarly, the mean absolute distance of b from the mean is |b-(a+b+c)/3| = |(2b-a-c)/3| and the mean absolute distance of b from the mean is |c-(a+b+c)/3| = |(2c-a-b)/3| . We have to find a,b,c such that |(2a-b-c)/3|+|(2b-a-c)/3|+|(2c-a-b)/3|=1 or,|(2a-b-c)|+ |(2b-a-c)| +|(2c-a-b)| = 3. Now, let a = -1 ,b = 1 and c = 1.5. Then this equation is satisfied. Thus, the 3 required numbers are -1,1 and 1.5.
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