PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoLet us look at an example to find standard deviation of ungrouped data by assumed mean method.
Example:
Find the standard deviation of the data 5, 8, 10, 11 and 12 which represents the number cookies in 5 bottles by assumed mean method.
Explanation:
Let n represent the number of values in the data.
n = 5
Let \overline x represent the mean of the given data.
Mean \overline x = \frac{\text{Sum of all the observations}}{\text{Total number of observations}}
\overline x = \frac{5 + 8 + 10 + 11 + 12}{5}
= \frac{46}{5}
= 9.2
Here, the mean is not an integer value.
So, let us find the standard deviation by assumed mean method.
Let A be the assumed mean, which is the middle most value.
Here, A = 10
Let x_{i} represent the marks scored by each student.
x_{i} | d_{i} = x_{i} - A = x_{i} - 10 | d_{i}^{2} |
5 | -5 | 25 |
8 | -2 | 4 |
10 | 0 | 0 |
11 | 1 | 1 |
12 | 2 | 4 |
\sum d_{i} = -4 | \sum d_{i}^{2} = 34 |
The formula to calculate the standard deviation by assumed mean method is given by:
\sigma = \sqrt{\frac{\sum d_{i}^{2}}{n}- \left(\frac{\sum d_{i}}{n}\right)^2} where d_{i} = x_{i} - A.
Substitute the known values in the above formula.
\sigma = \sqrt{\frac{34}{9}- \left(\frac{-4}{9}\right)^2}
= \sqrt{3.778 - (-0.444)^2}
= \sqrt{3.778 - 0.198}
= \sqrt{3.58}
= 1.892
\approx 1.89
Therefore, the standard deviation of the given data is 1.89.
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