If every term of the statistical data consisting of nterms is decreased by 2, then the mean of the data:

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Solution

Q.
If every term of the statistical data consisting of n terms is decreased by 2, then the mean of the data:

1 decreases by 2

2 remains unchanged

3 decreases by 2n

4 decreases by 1

Ans.
(1)

Let n terms of data be

$x_{1}, x_{2}, x_{3}, \dots, x_{n} . ∴ Mean (\bar{x}) = \frac{\sum_{i = 1}^{n} x_{i}}{n} N o w, w h e n e a c h t e r m i s d e c r e a s e d b y 2 . ∴ D a t a w i l l b e x_{1} - 2, x_{2} - 2, x_{3} - 2, \dots, x_{n} - 2 ∴ N e w m e a n = = \frac{\sum_{i = 1}^{n} (x_{i} - 2)}{n} = \frac{\sum_{i = 1}^{n} x_{i}}{n} - \frac{2 n}{n} = \bar{x} - 2 \Rightarrow " M e a n i s a l s o d e c r e a s e d b y 2 . "$

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