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QJEEM18Ma5e88: JEE Main 2018 Mathematics - Class 11 JEEM18Ma5e88 Solution: If the mean of the data : 7, 8, 9, 7, 8, 7, , 8 is 8, then the…

If the mean of the data : 7, 8, 9, 7, 8, 7, λ\lambda , 8 is 8, then the variance of this data is :

Multiple Choice Options

  • A 78{7 \over 8}
  • B 1
  • C 98{9 \over 8}
  • D 2

Step-by-Step Verified Solution

x‾\overline x = 7+8+9+7+8+7+λ+88{{7 + 8 + 9 + 7 + 8 + 7 + \lambda + 8} \over 8} = 8

⇒\Rightarrow    \,\,\, 54+λ8{{54 + \lambda } \over 8} = 8   ⇒\Rightarrow    λ\lambda = 10

Now variance = σ\sigma 2

= (7−8)2+(8−8)2+(9−8)2+(7−8)2+(8−8)2+(7−8)2+(10−8)2+(8−8)28{{{{\left( {7 - 8} \right)}^2} + {{\left( {8 - 8} \right)}^2} + {{\left( {9 - 8} \right)}^2} + {{\left( {7 - 8} \right)}^2} + {{\left( {8 - 8} \right)}^2} + {{\left( {7 - 8} \right)}^2} + {{\left( {10 - 8} \right)}^2} + {{\left( {8 - 8} \right)}^2}} \over 8}

⇒\Rightarrow    σ\sigma 2 = 1+0+1+1+0+1+4+08{{1 + 0 + 1 + 1 + 0 + 1 + 4 + 0} \over 8} = 88{8 \over 8} = 1

Hence, the variance is 1.

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