Find the mean and variance for each of the given data $\begin{matrix} x_{i} & 92 & 93 & 97 & 98 & 102 & 104 & 109 f_{i} & 3 & 2 & 3 & 2 & 6 & 3 & 3 \end{matrix}$

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Solution

$\begin{matrix} x_{i} & f_{i} & f_{i} x_{i} & (x_{i} - 100) & (x_{i} - 100)^{2} & f_{i} (x_{i} - 100)^{2} 92 & 3 & 276 & - 8 & 64 & 192 93 & 2 & 186 & - 7 & 49 & 97 97 & 3 & 291 & - 3 & 9 & 27 98 & 2 & 196 & - 2 & 4 & 8 102 & 6 & 612 & 2 & 4 & 24 104 & 3 & 312 & 4 & 16 & 48 109 & 3 & 327 & 9 & 81 & 243 22 & 2200 & 640 \end{matrix}$

Mean $(¯ ¯ ¯ x) = \frac{1}{N} \sum f_{i} x_{i} = \frac{1}{22} \times 2200 = 100$

Variance = $σ^{2} = \frac{1}{N} \sum_{i = 1}^{n} f_{i} (x_{i} - ¯ ¯ ¯ x)^{2}$

$= \frac{1}{22} \times 640 = 29.09$

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Find the mean and variance for each of the given data xi 92 93 97 98 102 104 109 fi 3 2 3 2 6 3 3

xi fi fixi (xi−100) (xi−100)2 fi(xi−100)2 92 3 276 −8 64 192 93 2 186 −7 49 97 97 3 291 −3 9 27 98 2 196 −2 4 8 102 6 612 2 4 24 104 3 312 4 16 48 109 3 327 9 81 243 22 2200 640 Mean (¯¯¯x)=1N∑fixi=122×2200=100 Variance = σ2=1N∑ni=1fi(xi−¯¯¯x)2 =122×640=29.09

Find the mean and variance for each of the given data $\begin{matrix} x_{i} & 92 & 93 & 97 & 98 & 102 & 104 & 109 f_{i} & 3 & 2 & 3 & 2 & 6 & 3 & 3 \end{matrix}$