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प्रश्न
The standard deviation of a data is ______ of any change in orgin, but is ______ on the change of scale.
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उत्तर
The standard deviation of a data is independent of any change in orgin, but is dependent. on the change of scale.
Explanation:
Since the standard deviation of any data is independent of any change in origin but is dependent of any change of scale.
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संबंधित प्रश्न
Find the mean and variance for the data.
6, 7, 10, 12, 13, 4, 8, 12
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The diameters of circles (in mm) drawn in a design are given below:
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| No. of circles | 15 | 17 | 21 | 22 | 25 |
Calculate the standard deviation and mean diameter of the circles.
[Hint: First make the data continuous by making the classes as 32.5 - 36.5, 36.5 - 40.5, 40.5 - 44.5, 44.5 - 48.5, 48.5 - 52.5 and then proceed.]
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\[\sigma = \sqrt{\frac{1}{n} \sum \left( x_i - X \right)^2_{}}\] and
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| x : | 4.5 | 14.5 | 24.5 | 34.5 | 44.5 | 54.5 | 64.5 |
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| Class: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
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| xi: | 1 ≤ x < 3 | 3 ≤ x < 5 | 5 ≤ x < 7 | 7 ≤ x < 10 |
| fi: | 6 | 4 | 5 | 1 |
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| Weight (in grams): | 200–201 | 201–202 | 202–203 | 203–204 | 204–205 | 205–206 |
| Frequency: | 13 | 27 | 18 | 10 | 1 | 1 |
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| Mean | 63.2 kg | 63.2 inch |
| Standard deviation | 5.6 kg | 11.5 inch |
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If v is the variance and σ is the standard deviation, then
The standard deviation of the data:
| x: | 1 | a | a2 | .... | an |
| f: | nC0 | nC1 | nC2 | .... | nCn |
is
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