Question 1Find the mean of the distribution- Class 1-3 3-5 5-7 7-10- Frequency 9 22 27 17- -

We first, find the class mark x_i of each class and then proceed as follows. [ Class amp; Class marks (x_i) amp; Frequency (f_i) ...

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Standard X

Mathematics

Finding Mean for Grouped Data When Class Intervals Are Given

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Question 1
Find the mean of the distribution.
$\begin{matrix} Class & 1 - 3 & 3 - 5 & 5 - 7 & 7 - 10 Frequency & 9 & 22 & 27 & 17 \end{matrix}$

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Solution

We first, find the class mark $x_{i}$ of each class and then proceed as follows.
$\begin{matrix} Class & Class marks (x_{i}) & Frequency (f_{i}) & f_{i} x_{i} 1 - 3 & 2 & 9 & 18 3 - 5 & 4 & 22 & 88 5 - 7 & 6 & 27 & 162 7 - 10 & 8.5 & 17 & 144.5 \sum f_{i} = 75 & \sum f_{i} x_{i} = 412.5 \end{matrix}$
Therefore, mean $(¯ x) = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{412.5}{75} = 5.5$
Hence, mean of the given distribution is 5.5.

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Question 1 Find the mean of the distribution. Class1−33−55−77−10Frequency9222717

We first, find the class mark xi of each class and then proceed as follows. Class & Class marks (xi) Frequency (fi)fixi1−329183−5422885−76271627−108.517144.5∑fi=75∑fixi=412.5 Therefore, mean (¯x)=∑fixi∑fi=412.575=5.5 Hence, mean of the given distribution is 5.5.

Question 1
Find the mean of the distribution.
$\begin{matrix} Class & 1 - 3 & 3 - 5 & 5 - 7 & 7 - 10 Frequency & 9 & 22 & 27 & 17 \end{matrix}$