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

NTA Abhyas 2020 · Mathematics · Statistics

The variance of the first 20 positive integral multiples of 4 is...

The variance of the first 2020 positive integral multiples of 44 is equal to

Options

  1. A532532
  2. B133133
  3. C266266
  4. D600600

Correct answer

A. 532532

Step-by-step solution

The numbers are 4,8,12........804, 8, 12 . . . . . . . . 80
Mean, (x¯)=4(1+2+3+......20)20=42( \overset{¯}{x} ) = \dfrac{4\left(1 + 2 + 3 + . . . . . . 20\right)}{20} = 42
Σxi2=42(12+22+......202)<br/>=16×20×21×416=45920Σ{x}_i^{2} = {4}^{2} \left({1}^{2} + {2}^{2} + {. . . . . . 20}^{2}\right)<br />=\dfrac{16 \times 20 \times 21 \times 41}{6} =45920
So, the variance is =Σxi220−(x−)2=2296−1764=532= \dfrac{Σ{x}_i^{2}}{20} - {( \overset{-}{x} )}^{2} =2296 - 1764 = 532
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