Data Collection Methods

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New answer posted•a year ago

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to:

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Answered by

a year ago

$\bar{x} = 6 = \frac{a + b + 8 + 5 + 10}{5} \Rightarrow a + b = 7$ …… (i)

and

$σ^{2} = \frac{a^{2} + b^{2} + 8^{2} + 5^{2} + 1 0^{2}}{5} - 6^{2} = 6.8$

⇒a² + b² = 25 ……. (ii)

From (i) and (ii) (a, b) = (3, 4) or (4, 3)

Now mean deviation about mean

$M = \frac{1}{5} (3 + 2 + 2 + 1 + 4) = \frac{12}{5}$

⇒ 25M = 60

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