Verified Solution • 2025–26 Session moderate

QJEEM18Ma91b9: JEE Main 2018 Mathematics - Class 11 JEEM18Ma91b9 Solution: The mean and the standard deviation(s.d.) of five observations…

The mean and the standard deviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

Multiple Choice Options

  • A 0
  • B 1
  • C 2
  • D 4

Step-by-Step Verified Solution

Here mean = x‾\overline x = 9

⇒\Rightarrow    x‾\overline x = ∑xin{{\sum {{x_i}} } \over n} = 9

⇒\Rightarrow    ∑xi{\sum {{x_i}} } = 9 ×\times 5 = 45

Now, standard deviation = 0

∴   \therefore\,\,\, all the five terms are same i.e.; 9

Now for changed observation

x‾new{\overline x _{new}} = 36+x55=10{{36 + {x_5}} \over 5} = 10

⇒\Rightarrow    x5 = 14

∴   \therefore\,\,\, σ\sigma new = ∑(xi−x‾new)2n\sqrt {{{\sum {{{\left( {{x_i} - {{\overline x }_{new}}} \right)}^2}} } \over n}}

= 4(9−10)2+(14−10)25\sqrt {{{4{{\left( {9 - 10} \right)}^2} + {{\left( {14 - 10} \right)}^2}} \over 5}} = 2

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