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  • If the mean and variance of eight numbers 3,7,9,12,13,20,x and y be 10 and 25 respectively, then  is equal to _____.Option: 1 54Option: 2

If the mean and variance of eight numbers 3,7,9,12,13,20,x and y be 10 and 25 respectively, then x\cdot y is equal to _____.
Option: 1 54
Option: 2 60
Option: 3 24
Option: 4 None

Answers (1)

best_answer

 

 

Mean -

Mean of the Ungrouped Data 

If n observations in data are x1, x2, x3, ……, xn, then arithmetic mean \mathit{\bar x} is given by    

\mathit{\bar x}=\frac{x_1+x_2+x_3+\ldots\dots +x_n }{n}=\frac{1}{n}\sum^{n}_{i=1}x_i

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Dispersion (Variance and Standard Deviation) -

Variance and Standard Deviation

The mean of the squares of the deviations from the mean is called the variance and is denoted by σ2 (read as sigma square).

Variance is a quantity which leads to a proper measure of dispersion. 

The variance of n observations x1 , x2 ,..., xn is given by

\sigma^{2}=\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2}

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\\\text{Mean}=\bar x=\frac{3+ 7+ 9+ 12+ 13+ 20 +x+ y}{8}=10\\\Rightarrow x+y=16\\\text{variance}\;\;\sigma^2=\frac{\sum (x_i)^2}{8}-(\bar x)^2\\\Rightarrow \frac{9 +49 +81+144+ 169 +400 +x^2 +y^2}{8}-100=25\\\Rightarrow x^2+y^2=148\\(x+y)^2=x^2+y^2+2xy\\xy=54

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Ritika Jonwal

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