Introduction to statistics

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The mean of the numbers a, b, 8, 5, 10, is 6 and the variance is $6.80$ . Then $a^{2} + b^{2} =$

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Solution

We have,
$Mean = 6 \Rightarrow \frac{a + b + 8 + 5 + 10}{5} = 6 \Rightarrow a + b = 7$ ... (i)
and, Variance =6.80
$\begin{array}{l} \Rightarrow \frac{1}{5} (a^{2} + b^{2} + 64 + 25 + 100) - 6^{2} = 6.80 \\ \Rightarrow a^{2} + b^{2} + 189 - 180 = 34 \Rightarrow a^{2} + b^{2} = 25 . . (i i) \end{array}$
Clearly, a= 3 and b = 4 satisfy these equations.

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Introduction to statistics

Remember concepts with our Masterclasses.

The mean of the numbers a, b, 8, 5, 10, is 6 and the variance is 6.80. Then a2+b2=

We have, Mean =6⇒a+b+8+5+105=6⇒a+b=7 ... (i) and, Variance =6.80⇒ 15a2+b2+64+25+100−62=6.80⇒ a2+b2+189−180=34⇒a2+b2=25 .. (ii)Clearly, a= 3 and b = 4 satisfy these equations.

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The mean of the numbers a, b, 8, 5, 10, is 6 and the variance is $6.80$ . Then $a^{2} + b^{2} =$