The mean of \( 6 \) distinct observations is \( 6.5 \) and their variance is \( 10.25 \). If \( 4 \) out of \( 6 \) observations are \( 2,4,5 \) and \( 7 \), then the remaining two observations are:
\( 8,13 \)
\( 1,20 \)
\( 3,18 \)
\( 10,11 \)
The first of the two samples in a group has \( 100 \) items with mean \( 15 \) and standard deviation \( 3 \). If the whole group has \( 250 \) items with mean \( 15.6 \) and standard deviation \( \sqrt{13.44} \), then the standard deviation of the second sample is:
An online exam is attempted by \( 50 \) candidates out of which \( 20 \) are boys. The average marks obtained by boys is \( 12 \) with variance \( 2 \). The variance of marks obtained by \( 30 \) girls is also \( 2 \). The average marks of \( 50 \) candidates is \( 15 \). If \( \mu \) is the average marks of girls and \( \sigma^{2} \) is varience of marks of \( 50 \) candidates, then \( \mu + \sigma^{2} \) is equal to ________.
Let the mean and variance of four numbers \( 3, 7, x \) and \( y \, (x>y) \) be \( 5 \) and \( 10 \) respectively. Then the mean of four numbers \( 3+2x, 7+2y, x+y \) and \( x-y \) is ________.
The mean and standard deviation of \( 20 \) observations were calculated as \( 10 \) and \( 2.5 \) respectively. It was found that by mistake one data value was taken as \( 25 \) instead of \( 35 \). If \( \alpha \) and \( \sqrt{\beta} \) are the mean and standard deviation respectively for correct data, then \( (\alpha, \beta) \) is:
