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If each observation of data is increased by ‘a’ then mean is increases by…………A) aB) a/2C) a2D) a + 1 |
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Answer» Correct option is: A) a Let \(x_1\) 's are original observations. Let there be n No of observations \(\therefore\) Sum of observations = \(n\overline x\) \(\Rightarrow\) \(\sum \limits_{i=1}^n x_i \) = \(n\overline x\) ....(1) If each observation of data is increased by a then (\(x_i+a\))'s are new observations of data. Sum of new observations = \(\sum \limits _{i=1}^n (x_i+9) = \sum \limits _{i=1}^n x_i + a \sum \limits _{i=1}^n 1\) = \(n\overline x\) + na = n (\(\overline x\) + a) \(\therefore\) Mean of new observations = \(\frac {sum}n = \frac {n(\overline x + a)}{n} = \overline x + a\) Hence, if each observation of data is increased by a, then new mean is increases by a. Correct option is: A) a |
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