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  • Suppose the mean score and standard deviation of students in class A are <im

Suppose the mean score and standard deviation of 100 students in class A are 40and a(>0) and the mean score and standad deviation are 30 respectively. If the mean and variance of the students' combined class scores are  50 and 350respectively, the sum of the class deviations is:

Option: 1

450


Option: 2

900


Option: 3

650


Option: 4

500


Answers (1)

best_answer
A B C
\fbox{$x_1$}=40 \fbox{$x_2$}=55 \fbox{$x_2$}=50
\sigma_1=\alpha \sigma_2=30-\alpha \sigma^2=350
n_1=100 n_2=n 100+n 

Now

\fbox{$X$}=\frac{100\times40+55n}{100+n}

Or, 5000+50n=4000+55n

Or, n=200

Now, {\sigma_1}^2=\frac{\sum{x_i}^2}{100}-{40}^2

Or, {\sigma_2}^2=\frac{\sum{x_j}^2}{100}-{55}^2

Or, 350=\sigma^2=\frac{\sum{x_i}^2+\sum{x_j}^2}{300}-\left(\fbox{$x$}\right)^2

2850\times3=\alpha^2+2\left(30-\alpha\right)^2+1600+6050

Or,\sigma^2+2\left(30-\sigma^2\right)+7650

Or , \sigma^2-40\sigma+300=0

Or, \sigma=1030

{\sigma_1}^2+{\sigma_2}^2={10}^2+{20}^2\ =500

Posted by

Riya

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