Multiple choice

The mean deviation from the mean $10$ of the data $6,7,10,12,13,\alpha,12,16$ is

  1. $3.5$
  2. $3.25$
  3. $3$
  4. $3.75$
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B Correct answer
Explanation

The mean deviation from the mean is the average of the absolute differences between each data point and the mean. With mean 10, the differences are |6-10|=4, |7-10|=3, |10-10|=0, |12-10|=2, |13-10|=3, |a-10|, |12-10|=2, |16-10|=6. Summing these and dividing by 8 gives 3.25, which implies |a-10|=2, meaning a=12 or 8.

AI explanation

First, find the sum of the known data points 6, 7, 10, 12, 13, 12, and 16, which equals 76, and add alpha to get a total sum of 76 plus alpha. Since the mean is 10 for the 8 numbers, the total sum must be 80, meaning alpha is 4. The absolute deviations of the 8 values from the mean of 10 are 4, 3, 0, 2, 3, 6, 2, and 6. Summing these gives 26, and dividing by 8 results in a mean deviation of 3.25.

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