Class 11

Math

JEE Main Questions

Statistics

The mean of 100 numbers observations is 50 and their standards deviation is 5. The sum of all squares of all the observations is (a)50,000 (b) 250,000 (c) 252500 (d) 255000

Standard deviation,$(σ)=5$

$∴$ Variance $=σ_{2}=5_{2}=25$

$∴25=n1 [∑(x_{i}−X_{2})]$

Here, $n=100$

$∴25=1001 [∑x_{i}−100(50)_{2}]$

$⇒2500=∑x_{i}−100(50)_{2}$

$⇒∑x_{i}=250000+2500=252500$

$∴∑x_{i}=252500.$