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Finding Mean for Grouped Data When Class Intervals Are Given

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Question 1
In the formula $¯ x = a + \frac{\sum f_{i} d_{i}}{\sum f_{i}}$ , for finding the mean of grouped data $d_{i}^{'} s$ are deviation from a of
(a) lower limits of the classes
(b) upper limits of the classes
(c) mid-points of the classes
(d) frequencies of the class marks

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Solution

We know that, $d_{i} = x_{i} - a$
i.e., $d_{i}^{'} s$ are the deviation from a of mid-points of the classes.

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Q. In the formula,

x = \{A + \frac{\sum f_{i} d_{i}}{\sum f_{i}}\}

for finding the mean of the grouped data, the d_i's are the deviations from A of
(a) lower limits of the classes
(b) upper limits of the classes
(c) midpoints of the classes
(d) none of these

Q. In the formula

\bar{X} = a + \frac{Σ f_{i} d_{i}}{Σ f_{i}}

, for finding the mean of grouped data

{d_{i}}^{'^{s}}

are derivations from

a

of
(a) lower limits of classes (b) upper limits ofclasses
(c) mid-points of classes (d) frequency of the class marks

Q. Question 22
For drawing a frequency polygon of a continuous frequency distribution, we plot the points whose ordinates are the frequencies of the respective classes and abcissae are, respectively:

A) Upper limits of the classes
B) Lower limits of the classes
C) Class marks of the classes
D) Upper limits of preceding classes

Q. Question 2
While computing mean of grouped data, we assume that the frequencies are
(a) evenly distributed over all the classes
(b) centred at the class marks of the classes
(c) centred at the upper limits of the classes
(d) centred at the lower limits of the classes

d_{i}

is the deviation of a class mark

y_{i}

from ‘a’ the assumed mean and

f_{i}

is the frequency, if

M_{g} = x + \frac{1}{\sum f_{i}} (\sum f_{i} d_{i})

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Finding Mean for Grouped Data When Class Intervals Are Given

Standard X Mathematics

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