Vedclass

Find the mean and variance for the data

${x_i}$ $92$ $93$ $97$ $98$ $102$ $104$ $109$
${f_i}$ $3$ $2$ $3$ $2$ $6$ $3$ $3$

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The data is obtained in tabular form as follows.

${x_i}$ ${f_i}$ ${f_i}{x_i}$ ${{x_i} - \bar x}$ ${\left( {{x_i} - \bar x} \right)^2}$ ${f_i}{\left( {{x_i} - \bar x} \right)^2}$
$92$ $3$ $276$ $-8$ $64$ $192$
$93$ $2$ $186$ $-7$ $49$ $98$
$97$ $3$ $291$ $-3$ $9$ $27$
$98$ $2$ $196$ $-2$ $4$ $8$
$102$ $6$ $612$ $2$ $4$ $24$
$104$ $3$ $312$ $4$ $16$ $48$
$109$ $3$ $327$ $9$ $81$ $243$
  $22$ $2200$     $640$

Here,    $N = 22,\sum\limits_{i = 1}^7 {{f_i}{x_i}}  = 2200$

$\therefore \bar x = \frac{1}{n}\sum\limits_{i = 1}^7 {{f_i}{x_i}}  = \frac{1}{{22}} \times 2200 = 100$

Variance $\left( {{\sigma ^2}} \right) = \frac{1}{N}\sum\limits_{i = 1}^7 {{f_i}{{\left( {{x_i} - \bar x} \right)}^2} = } \frac{1}{{22}} \times 640 = 29.09$

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