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(A) To find the variance,we first calculate the mean and the sum of squares of the values.$x_i$$f_i$$f_i x_i$$f_i x_i^2$$5$$3$$15$$75$$6$$7$$42$$252$$

Vedclass · Accepted Answer

$2.85$

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(A) To find the variance,we first calculate the mean and the sum of squares of the values.$x_i$$f_i$$f_i x_i$$f_i x_i^2$$5$$3$$15$$75$$6$$7$$42$$252$$7$$4$$28$$196$$8$$2$$16$$128$$10$$4$$40$$400$Total$N=20$$\sum f_i x_i = 141$$\sum f_i x_i^2 = 1051$The formula for variance is $\sigma^2 = \frac{\sum f_i x_i^2}{N} - \left(\frac{\sum f_i x_i}{N}\right)^2$.Substituting the values:$\sigma^2 = \frac{1051}{20} - \left(\frac{141}{20}\right)^2$$\sigma^2 = 52.55 - (7.05)^2$$\sigma^2 = 52.55 - 49.7025$$\sigma^2 = 2.8475 \approx 2.85$.

For the following frequency distribution,find the variance:
$X$ $5$ $6$ $7$ $8$ $10$
Frequency $3$ $7$ $4$ $2$ $4$

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For the following frequency distribution,find the variance:$X$$5$$6$$7$$8$$10$Frequency$3$$7$$4$$2$$4$