The mean of four numbers is 5, and the mean deviation is 3. Find the fourth number if the mean deviation of the first three numbers is 2
Let the four numbers be \(a, b, c, d\).
- Mean of the four numbers = 5
→ a + b + c + d = 20
- Mean deviation of the four numbers = 3
Mean deviation = \(\frac{|a-5| + |b-5| + |c-5| + |d-5|}{4} = 3\)
→ Sum of absolute deviations = 12
- Mean deviation of the first three numbers a, b, c = 2
→ \(\frac{|a-5| + |b-5| + |c-5|}{3} = 2\)
→ Sum of absolute deviations for first three = 6
- Therefore, absolute deviation for the fourth number:
|d - 5| = 12 - 6 = 6
The fourth number = 6 + 5 = 11.
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