The mean of 10 numbers 7 $\times$ 8, 10 $\times$ 10, 13 $\times$ 12, 16 $\times$ 14, ....... is ____________.
Answer (integer)
398
Solution
7 $\times$ 8, 10 $\times$ 10, 13 $\times$ 12, 16 $\times$ 14 ........<br><br>T<sub>n</sub> = (3n + 4) (2n + 6) = 2(3n + 4) (n + 3)<br><br>= 2(3n<sup>2</sup> + 13n + 12) = 6n<sup>2</sup> + 26n + 24<br><br>S<sub>10</sub> = $$\sum\limits_{n = 1}^{10} {{T_n}} = 6\sum\limits_{n = 1}^{10} {{n^2}} + 26\sum\limits_{n = 1}^{10} n + 24\sum\limits_{n = 1}^{10} 1 $$<br><br>$$ = {{6(10 \times 11 \times 21)} \over 6} + 26 \times {{10 \times 11} \over 2} + 24 \times 10$$<br><br>$= 10 \times 11(21 + 13) + 240$<br><br>= 3980<br><br>Mean $= {{{S_{10}}} \over {10}} = {{3980} \over {10}} = 398$
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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