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in Statistics by (35.6k points)
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The mean of a data is 9. If each observation is multiplied by 3 and then 1 is added to each result, then the mean of new observation is………

A) 19 

B) 20 

C) 28 

D) 30

2 Answers

+1 vote
by (66.4k points)
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Best answer

Correct option is: C) 28

Let \(x_1\)'s are observations of the original data .

Given that mean of data is 9.

Let total no. of observation be n.

\(\therefore\) Sum of observations = n\(\overline x\) = 9n

\(\Rightarrow\) \(\sum \limits _{i=1}^n x_i\) = 9n ....(1)

Since, each observation ( \(x_1\)'s) are multiplied by 3 and then 1 is added to each result.

\(\therefore\) (\(3x_i + 1\))'s are new observations.

\(\therefore\) Mean of formed data = \(\frac {sum\, of \,new \,observations}n\)

\(\frac {\sum \limits_{i=1}^n (3x_i+1)}{n}\)

\(\frac {\sum \limits_{i=1}^n 3x_i + \sum \limits_{i=1}^n 1}{n}\)

\(\frac {3\sum \limits_{i=1}^n x_i +n}{n}\) (\(\because\) \(\sum \limits_{i=1}^n 1 = 1 + 1+1+...+1 (n \, times) = n\))

\(\frac {3\times 9n+n}{n} \) (From (i))

\(\frac {28n}{n} = 28\) 

Hence, the mean of new observations is 28.

+1 vote
by (34.5k points)

Correct option is: C) 28

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