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Find the Mean, Variance and Standard Deviation for the Data: 6, 7, 10, 12, 13, 4, 8, 12. - Mathematics

Find the mean, variance and standard deviation for the data:

6, 7, 10, 12, 13, 4, 8, 12.

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Solution

6,7,10,12,13,4,8,12

\[\text{ Mean } = \frac{6 + 7 + 10 + 12 + 13 + 4 + 8 + 12}{8}\]

\[ = \frac{72}{8}\]

\[ = 9\]

\[x_i\]
\[\left( x_i - X \right) = \left( x_i - 9 \right)\]
 
\[\left( x_i - X \right)^2\]
6 -3 9
7 -2 4
10 1 1
12 3 9
13 4 16
4
 
- 5
25
8
 
-1
1
12 3 9
   
 
\[\sum^8_{i = 1} \left( x_i - X \right)^2 = 74\]

n = 8

\[\therefore \text{ Variance } \left( X \right) = \frac{\sum^8_{i = 1} \left( x_i - X \right)^2}{n}\]

\[ = \frac{74}{8} \]

\[ = 9 . 25\]

\[\text{ Standard deviation }= \sqrt{\text{Variance} \left( X \right)} \]

\[ = \sqrt{9 . 25} \]

\[ = 3 . 04\]

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.4 | Q 1.2 | Page 28
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