If x_{i} are the midpoints of the class inter | vedclass

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(A) The mean $\bar{x}$ of grouped data is given by the formula $\bar{x} = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$,where $n = \sum f_{i}$.This can be rewr

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(A) The mean $\bar{x}$ of grouped data is given by the formula $\bar{x} = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$,where $n = \sum f_{i}$.This can be rewritten as $\sum f_{i} x_{i} = n \bar{x}$.We need to evaluate the sum $\sum (f_{i} x_{i} - f_{i} \bar{x})$.Using the properties of summation,we get $\sum f_{i} x_{i} - \sum f_{i} \bar{x}$.Since $\bar{x}$ is a constant,we can take it out of the summation: $\sum f_{i} x_{i} - \bar{x} \sum f_{i}$.Substituting $\sum f_{i} x_{i} = n \bar{x}$ and $\sum f_{i} = n$,we get $n \bar{x} - \bar{x} (n) = n \bar{x} - n \bar{x} = 0$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$10$	$12$	$13$	$16$	$9$

Number of seats	$100-104$	$104-108$	$108-112$	$112-116$	$116-120$
Frequency	$15$	$20$	$32$	$18$	$15$

Class	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$12$	$30$	$x$	$65$	$y$	$25$	$18$

If $x_{i}$ are the midpoints of the class intervals of grouped data,$f_{i}$ are the corresponding frequencies,and $\bar{x}$ is the mean,then $\sum (f_{i} x_{i} - f_{i} \bar{x})$ is equal to

Similar Questions

Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$
Frequency $10$ $12$ $13$ $16$ $9$

For the frequency distribution given above,which of the following is false?

For a given frequency distribution,the frequencies of the first,second,and third class are $8$,$15$,and $18$ respectively. Then,the cumulative frequency of the third class is $\ldots \ldots \ldots \ldots .$

An aircraft has $120$ passenger seats. The number of seats occupied during $100$ flights is given in the following table:

Number of seats $100-104$ $104-108$ $108-112$ $112-116$ $116-120$

Frequency $15$ $20$ $32$ $18$ $15$

Determine the mean number of seats occupied over the flights. (in $.92$)

For some given data,if $M + \bar{x} = 32$ and $M - \bar{x} = 2$,then $Z = \ldots \ldots \ldots$

The median of the following frequency distribution is $46$ and the total frequency is $230$. Find the missing frequencies $x$ and $y$.

Class $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$

Frequency $12$ $30$ $x$ $65$ $y$ $25$ $18$

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