The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is :

Question

The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is : (A) 8.25 (B) 8.50 (C) 8.00 (D) 9.00

Tardigrade Admin · Accepted Answer

displaystyle∑i=1100 x i= 400 displaystyle∑i=1100 xi 2=2475 variance σ2=(∑ x i2/N)-((∑ x1/N))2 32+42+52 9+16+25+50 =(2475/97)-((388/97))2 (2425/97)-16 (2425-1552/97)=(873/97) =(9)

Q. The sum of $100$ observations and the sum of their squares are $400$ and $2475$ , respectively. Later on, three observations, $3, 4$ and $5$ , were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is :

8.25

8.50

8.00

9.00

$i = 1 \sum 100 x i = 400 i = 1 \sum 100 x i^{2} = 2475$
variance $σ^{2} = \frac{\sum x i ^{2}}{N} - (\frac{\sum x _{1}}{N})^{2} 3^{2} + 4^{2} + 5^{2}$
$9 + 16 + 25 + 50$
$= \frac{2475}{97} - (\frac{388}{97})^{2}$
$\frac{2425}{97} - 16$
$\frac{2425 - 1552}{97} = \frac{873}{97}$
$= (9)$

Q. The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3,4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is :