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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Statistics

NTA Abhyas 2020 · Mathematics · Statistics

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

The mean of a data set comprising of 16\text{16} observations is 16\text{16}. If one of the observation valued 16\text{16} is deleted and three new observations valued 3, 4\text{3, 4} and 5\text{5} are added to the data, then the mean of the resultant data is

Options

  1. A14.0\text{14.0}
  2. B16.8\text{16.8}
  3. C16.0\text{16.0}
  4. D15.8\text{15.8}

Correct answer

A. 14.0\text{14.0}

Step-by-step solution

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

⇒∑i=115xi+16=256⇒\mathop{∑}_{i = 1 }^{15} {x}_{i}+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{\text{252}}{\text{18}} = \text{14}
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