Verified Solution • 2025–26 Session moderate

QJEEM19Ma3c6b: JEE Main 2019 Mathematics - Class 11 JEEM19Ma3c6b Solution: A student scores the following marks in five tests : 45, 54,…

A student scores the following marks in five tests :

45, 54, 41, 57, 43.

His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is

Multiple Choice Options

  • A 1003100 \over {\sqrt 3}
  • B 10310 \over {\sqrt 3}
  • C 10310 \over3
  • D 1003100 \over3

Step-by-Step Verified Solution

Let the score in the sixth test = x

Given, Mean ( x‾\overline x ) = 48

⇒\Rightarrow 45+54+41+57+43+x6{{45 + 54 + 41 + 57 + 43 + x} \over 6} = 48

⇒\Rightarrow x = 48

Standard deviation (SD)

= ∑i=1N(xi−x‾)2N\sqrt {{{\sum\limits_{i = 1}^N {{{\left( {{x_i} - \overline x } \right)}^2}} } \over N}}

= (45−48)2+(54−48)2+(41−48)2+(57−48)2+(43−48)2+(48−48)26

= 9+36+49+81+256\sqrt {{{9 + 36 + 49 + 81 + 25} \over 6}}

= 2006\sqrt {{{200} \over 6}}

= 1003\sqrt {{{100} \over 3}}

= 103{{10} \over {\sqrt 3 }}

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