For the frequency distribution :
Variate $( x )$ | $x _{1}$ | $x _{1}$ | $x _{3} \ldots \ldots x _{15}$ |
Frequency $(f)$ | $f _{1}$ | $f _{1}$ | $f _{3} \ldots f _{15}$ |
where $0< x _{1}< x _{2}< x _{3}<\ldots .< x _{15}=10$ and
$\sum \limits_{i=1}^{15} f_{i}>0,$ the standard deviation cannot be
$2$
$1$
$4$
$6$
The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three observations are $1, 2$ and $6$, the other two observations are
One set containing five numbers has mean $8$ and variance $18$ and the second set containing $3$ numbers has mean $8$ and variance $24$. Then the variance of the combined set of numbers is
From the data given below state which group is more variable, $A$ or $B$ ?
Marks | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ |
Group $A$ | $9$ | $17$ | $32$ | $33$ | $40$ | $10$ | $9$ |
Group $B$ | $10$ | $20$ | $30$ | $25$ | $43$ | $15$ | $7$ |
The $S.D$. of the first $n$ natural numbers is
The variance of first $50$ even natural numbers is