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UGC NET Paper 2: Education November 2017

Option 3 : (53, 10)

Official Paper 1: Held on 24 Sep 2020 Shift 1

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50 Questions
100 Marks
60 Mins

Mean is the sum of all quantities divided by no of quantities. The simple average of the numbers.

Standard deviation is used to measure how deviated or dispersed the numbers are with respect to the mean in the same set of data.

__Important Points__

Let x_{1}, x_{2}, x_{3, }x_{4} be the observations, then the mean of these observations will be \({ x_1+ x_2 + x_3 + x_4} \over 4\)

each score is increased by 3

⇒ Mean = \({ (x_1 +3)+ (x_2 + 3)+ (x_3 + 3)+ (x_4 + 3)} \over 4\)

⇒ Mean = \({ x_1+ x_2 + x_3 + x_4 + 12} \over 4\)

⇒ Mean = \({{ x_1+ x_2 + x_3 + x_4} \over 4 } + {12 \over 4}\)

⇒ Mean = \({{ x_1+ x_2 + x_3 + x_4} \over 4 } + {3}\)

**∴ The mean also increases by 3. So, the new mean is 53.**

When adding or subtracting a constant from a distribution, the mean will change by the same amount as the constant. The standard deviation will remain unchanged. This fact is true because, again, we are just shifting the distribution up or down the scale. We do not affect the distance between values. **Therefore If each score increases or decreases by the same value the standard deviation remains 10.**

__Additional Information__

- If each term of data is either increased or decreased by the same constant number then the mean of the data is also increased or decreased by the same constant term respectively$.$

- If each term of data is either multiplied or divided by the same constant number then the mean of the data is also multiplied or divided by the same constant term respectively$.$

- If each term of data is either increased or decreased by the same constant number then the standard deviation of the data remains unchanged$.$
- If each term of data is either multiplied or divided by the same constant number then the standard deviation of the data is also multiplied or divided by the same constant term respectively$.$