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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class11  >>  Statistics
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Q)

A group of 10 items has arithmatic mean 6. If the arithmatic mean of 4 of these remaining item is 7.5 then the mean of the remaining item is

$\begin {array} {1 1} (A)\;6.5 & \quad (B)\;5.5 \\ (C)\;4.5 & \quad (D)\;5.0 \end {array}$

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A)
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Since $ \large\frac{ \sum_{i=1}^{10} x_1}{10}=6$
$ \Rightarrow \sum_{i=1}^{10}x_i=60$
$ \large\frac{ \sum_{i=1}^{4} x_1}{10}=7.5$
$ \sum_{i=1}^{4}x_i=30$
$ \therefore \sum_{i=5}^{10}x_1=60-30$
$ = 30$
$ \Rightarrow $ Mean of remaining items = $ \large\frac{30}{6}$
$ = 5$
Ans : (D)
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