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JEE Main 20154 April
Exam
JEE Main
Year
2015
Date
4 April
Subject
Mathematics
Chapter
Statistics

JEE Main 2015 · 4 April · Mathematics · Statistics

The mean of a data set comprising of 16 observations is 16 . If one...

The mean of a data set comprising of 1616 observations is 1616. If one of the observation value 1616 is deleted and three new observations valued 3,43 , 4 and 55 are added to the data, then the mean of the resultant data is

Options

  1. A14.014 .0
  2. B16.816 .8
  3. C16.016 .0
  4. D15.815 .8

Correct answer

A. 14.014 .0

Step-by-step solution

Given, (∑i=115xi)+1616=16\dfrac{( \mathop{∑}_{i = 1 }^{15} {x}_{i} ) + 16}{16} = 16

⇒⇒ ∑i=115xi\mathop{∑}_{i = 1}^{15}{x}_{i} +16=256+16 = \text{256}

⇒∑i=115xi=240⇒ \mathop{∑}_{i = 1}^{15}{x}_{i} = 240

Required mean =∑i=115xi+3+4+518=240+3+4+518= \dfrac{\mathop{∑}_{i = 1}^{15}{x}_{i} + 3 + 4 + 5}{18} = \dfrac{240 + 3 + 4 + 5}{18}

=25218=14= \dfrac{252}{18} = 14
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