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 :
Solution
<p>$\because$ $\overline x = 6 = {{a + b + 8 + 5 + 10} \over 5} \Rightarrow a + b = 7$ ...... (i)</p>
<p>And ${\sigma ^2} = {{{a^2} + {b^2} + {8^2} + {5^2} + {{10}^2}} \over 5} - {6^2} = 6.8$</p>
<p>$\Rightarrow {a^2} + {b^2} = 25$ ..... (ii)</p>
<p>From (i) and (ii) (a, b) = (3, 4) or (4, 3)</p>
<p>Now mean deviation about mean</p>
<p>$M = {1 \over 5}(3 + 2 + 2 + 1 + 4) = {{12} \over 5}$</p>
<p>$\Rightarrow 25M = 60$</p>
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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