The frequency distribution:
$\begin{array}{|l|l|l|l|l|l|l|} \hline X & A & 2 A & 3 A & 4 A & 5 A & 6 A \\ \hline f & 2 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{array}$
where $A$ is a positive integer, has a variance of $160 .$ Determine the value of $A$.
$\begin{array}{|c|c|c|c|} \hline x & f_{i} & f_{1} x_{i} & f x_{i}^{2} \\ \hline A & 2 & 2 A & 2 A^{2} \\ \hline 2 A & 1 & 2 A & 4 A^{2} \\ \hline 3 A & 1 & 3 A & 9 A^{2} \\ \hline 4 A & 1 & 4 A & 16 A^{2} \\ \hline 5 A & 1 & 5 A & 25 A^{2} \\ \hline 6 A & 1 & 6 A & 36 A^{2} \\ \hline \text { Total } & n=7 & \Sigma f_{i}=22 A & \Sigma f_{i}^{2}=92 A^{2} \\ \hline \end{array}$
$\therefore \quad \sigma^{2}=\frac{\Sigma f_{t} x_{1}^{2}}{n}-\left(\frac{\Sigma f_{1} x_{1}}{n}\right)^{2}$
$\Rightarrow \quad 160=\frac{92 A^{2}}{7}-\left(\frac{22 A}{7}\right)^{2} \Rightarrow 160=\frac{92 A^{2}}{7}-\frac{484 A^{2}}{49}$
$\Rightarrow \quad 160=(644-484) \frac{A^{2}}{49} \Rightarrow 160=\frac{160 A^{2}}{49}$
$\Rightarrow \quad A^{2}=49 \quad \therefore \quad A=7$
The mean and variance of $5$ observations are $5$ and $8$ respectively. If $3$ observations are $1,3,5$, then the sum of cubes of the remaining two observations is
The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours. Find the overall standard deviation.
If the standard deviation of the numbers $ 2,3,a $ and $11$ is $3.5$ then which of the following is true ?
What is the standard deviation of the following series
class |
0-10 |
10-20 |
20-30 |
30-40 |
Freq |
1 |
3 |
4 |
2 |
If the variance of the frequency distribution is $160$ , then the value of $\mathrm{c} \in \mathrm{N}$ is
$X$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
$f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |