For two data sets, each of size $5$, the variances are given to be $4$ and $5$ and the corresponding means are given to be $2$ and $4$, respectively. The variance of the combined data set is

  • [AIEEE 2010]
  • A

    $\frac{{11}}{2}$

  • B

    $6$

  • C

    $\frac{{13}}{2}$

  • D

    $\frac{5}{2}$

Similar Questions

The mean and standard deviation of a group of $100$ observations were found to be $20$ and $3,$ respectively. Later on it was found that three observations were incorrect, which were recorded as $21,21$ and $18 .$ Find the mean and standard deviation if the incorrect observations are omitted.

Calculate the mean, variance and standard deviation for the following distribution:

Class $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$
$f_i$ $3$ $7$ $12$ $15$ $8$ $3$ $2$

If the variance of the following frequency distribution is $50$ then $x$ is equal to:

Class $10-20$ $20-30$ $30-40$
Frequency $2$ $x$ $2$

  • [JEE MAIN 2020]

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.

Find the mean and variance of the frequency distribution given below:

$\begin{array}{|l|l|l|l|l|} \hline x & 1 \leq x<3 & 3 \leq x<5 & 5 \leq x<7 & 7 \leq x<10 \\ \hline f & 6 & 4 & 5 & 1 \\ \hline \end{array}$