Introduction to statistics

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Calculate variance for the following distribution.

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Solution

Let the assumed mean A = 65. Here, h = 10. We obtain the following table from the given data.

$\begin{array}{l} Therefore \bar{x} = A + \frac{\sum f_{i} y_{i}}{50} \times h = 65 - \frac{15}{50} \times 10 = 62 \\ Variance σ^{2} = \frac{h^{2}}{N^{2}} [N Σ f_{i} y_{i}^{2} - {(Σ f_{i} y_{i})}^{2}] \\ = \frac{(10)^{2}}{(50)^{2}} [50 \times 105 - (- 15)^{2}] \\ = \frac{1}{25} [5250 - 225] = 201 \end{array}$

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Introduction to statistics

Remember concepts with our Masterclasses.

Calculate variance for the following distribution.

Let the assumed mean A = 65. Here, h = 10. We obtain the following table from the given data. Therefore x¯=A+∑fiyi50×h=65−1550×10=62 Variance σ2=h2N2NΣfiyi2−Σfiyi2 =(10)2(50)250×105−(−15)2 =125[5250−225]=201

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