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Properties of Measures of Central Tendency

Fill in the b...

Question

Fill in the blank:
An arithmetic mean of grouped data is calculated by direct method formula is __________ .

¯ x = \frac{\sum f_{i} + x_{i}}{\sum f_{i}}

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¯ x = \frac{\sum f_{i} x_{i}}{\sum f_{i}}

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¯ x = \frac{\sum f_{i} - x_{i}}{\sum f_{i}}

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¯ x = \frac{\sum f_{i} \times x_{i}}{\sum f_{i}}

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Solution

The correct option is B $¯ x = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$
Arithmetic mean of grouped data direct method formula, $¯ x = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$ ,
where, $¯ x =$ Mean of the given data
$f_{i} =$ Sum of all the frequencies
$f_{i} x_{i} =$ Sum of the product of frequencies

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Similar questions

The mid - points of class intervals $x_{i}$ along with respective frequencies $f_{i}$ for recorded observations are given. Calculate the mean deviations about mean $¯ ¯ ¯ x$

Q. If

x_{i}

's are the mid points of the class intervals of grouped data,

f_{1}

's are the corresponding frequencies and

¯ x

is the mean, then

\sum (f_{i} x_{i} - ¯ x)

is equal to

Q. Question 3
If

x_{i}^{'} s

are the mid-points of the calss intervals of grouped data,

f_{i}^{'} s

are the corresponding frequencies and

¯ x

is the mean, then

\sum (f_{i} x_{i} - ¯ x)

is equal to
(a) 0
(b) -1
(c) 1
(d) 2

Q. Question 4
In the formula

¯ x = a + h (\frac{\sum f_{i} u_{i}}{\sum f_{i}}),

for finding the mean of grouped frequency distribution

u_{i}

is equal to
(a)

\frac{x_{i} + a}{h}

(b)

x_{i} + a

(c)

\frac{x_{i} + a}{h}

(a)

\frac{a - x_{i}}{h}

In the formula $¯ x = A + \frac{\sum f_{i} d_{i}}{\sum f_{i}}$ , the A stands for assumed mean.

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Fill in the blank:An arithmetic mean of grouped data is calculated by direct method formula is __________ .

The correct option is B ¯x=∑fixi∑fiArithmetic mean of grouped data direct method formula, ¯x=∑fixi∑fi,where, ¯x= Mean of the given datafi= Sum of all the frequenciesfixi= Sum of the product of frequencies

Fill in the blank:
An arithmetic mean of grouped data is calculated by direct method formula is __________ .

The correct option is B $¯ x = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$
Arithmetic mean of grouped data direct method formula, $¯ x = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$ ,
where, $¯ x =$ Mean of the given data
$f_{i} =$ Sum of all the frequencies
$f_{i} x_{i} =$ Sum of the product of frequencies