(A) The mean $(\bar{x})$ of grouped data using the direct method is calculated by the formula: $\bar{x} = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$,where $

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$\bar{x}=\frac{\Sigma f_{i} x_{i}}{\Sigma f_{i}}$

(A) The mean $(\bar{x})$ of grouped data using the direct method is calculated by the formula: $\bar{x} = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$,where $f_{i}$ is the frequency of the $i^{th}$ class interval and $x_{i}$ is the class mark (midpoint) of the $i^{th}$ class interval. The sum $\sum f_{i}$ is often denoted by $N$ or $n$,representing the total number of observations.

Class 10 Mathematics Statistics Mix Examples - Statistics

Easy

The formula to find the mean of a grouped data by the direct method is .........

A
$\bar{x}=\frac{\Sigma f_{i} x_{i}}{\Sigma f_{i}}$
B
$\bar{x}=\frac{\Sigma x_{i}}{\Sigma f_{i}}$
C
$\bar{x}=\frac{\Sigma f_{i} x_{i}}{n}$
D
$\bar{x}=\frac{\Sigma f_{i} x_{i}}{n} \times c$

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Mix Examples - Statistics

The mean of the following frequency distribution is $28.5$ and the total frequency is $60$. Find the missing frequencies $f_{1}$ and $f_{2}$.

Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$

Frequency $6$ $f_1$ $20$ $15$ $f_2$ $4$

Medium

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The mean of $5$ observations is $16$. If an observation $5$ is replaced by $-5$,the new mean is ...........

Medium

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In the formula $M = l + \frac{(\frac{n}{2} - cf)}{f} \times c$ for the median,$cf = \ldots \ldots \ldots$

Easy

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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 $.92$)

Medium

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For a given frequency distribution,$A=49.5, \Sigma f_{i}=40, \Sigma f_{i} u_{i}=-5$ and $c=20$. Then,mean $\bar{x}=$ ............

Easy

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Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$6$	$f_1$	$20$	$15$	$f_2$	$4$

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

The formula to find the mean of a grouped data by the direct method is .........

Similar Questions

The mean of the following frequency distribution is $28.5$ and the total frequency is $60$. Find the missing frequencies $f_{1}$ and $f_{2}$. Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ Frequency $6$ $f_1$ $20$ $15$ $f_2$ $4$

The mean of $5$ observations is $16$. If an observation $5$ is replaced by $-5$,the new mean is ...........

In the formula $M = l + \frac{(\frac{n}{2} - cf)}{f} \times c$ for the median,$cf = \ldots \ldots \ldots$

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 a given frequency distribution,$A=49.5, \Sigma f_{i}=40, \Sigma f_{i} u_{i}=-5$ and $c=20$. Then,mean $\bar{x}=$ ............

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The mean of the following frequency distribution is $28.5$ and the total frequency is $60$. Find the missing frequencies $f_{1}$ and $f_{2}$.

Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$

Frequency $6$ $f_1$ $20$ $15$ $f_2$ $4$

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 $.92$)