The average marks of $10$ students in a class was $60$ with a standard deviation of $4$,while the average marks of another $10$ students was $40$ with a standard deviation of $6$. If all the $20$ students are taken together,their combined standard deviation will be:

  • A
    $5$
  • B
    $7.5$
  • C
    $9.8$
  • D
    $11.2$

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Similar Questions

If the standard deviation of the numbers $2, 3, a$,and $11$ is $3.5$,then which of the following is true?

The variance of the following frequency distribution is:
Classes$0-10$$10-20$$20-30$$30-40$$40-50$$50-60$
Frequency$11$$29$$18$$4$$5$$3$

In an experiment with $15$ observations,the results were available as $\sum X^2 = 2830$ and $\sum X = 170$. One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. The corrected variance is:

The marks obtained by students $A$ and $B$ in $3$ examinations are given below:
Marks of $A$ $30, 20, 40$
Marks of $B$ $70, 0, 5$

The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is:

For the frequency distribution:
Variate $(x)$ $x_{1}$ $x_{2}$ $x_{3} \ldots x_{15}$
Frequency $(f)$ $f_{1}$ $f_{2}$ $f_{3} \ldots f_{15}$

where $0 < x_{1} < x_{2} < x_{3} < \ldots < x_{15} = 10$ and $\sum_{i=1}^{15} f_{i} > 0$,the standard deviation cannot be:

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