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JEE Main 201912 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
12 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Statistics

JEE Main 2019 · 12 January · Morning Shift · Mathematics · Statistics

If the sum of the deviations of 50 observations from 30 is 50 ,...

If the sum of the deviations of 5050 observations from 3030 is 5050, then the mean of these observations is :

Options

  1. A3030
  2. B5151
  3. C5050
  4. D3131

Correct answer

D. 3131

Step-by-step solution

Let the observations be x1,x2,...,x50{x}_{1}, {x}_{2}, . . . , {x}_{50}.

Given \left({x}_{1} - 30\right) + \left({x}_{2} - 30\right) + . . . . . + \left({x}_{50} - 30\right) = 50<br/><br/><br /><br />⇒ {x}_{1} + {x}_{2} + . . . . . + {x}_{50} = 50 + \left(30 \times 50\right) = 1550<br/><br/>Now,Mean<br /><br />Now, Mean= \dfrac{{x}_{1} + {x}_{2} + . . . . + {x}_{50}}{50} = \dfrac{1550}{50} = 31$.
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