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

The combined mean is (10 times 60 plus 10 times 40) divided by 20, which equals 50. The combined variance is found by adding the within-group variances and the variance of the group means: 16 plus 36 plus 100 equals 152. The combined standard deviation is the square root of 152, which is approximately 11.5.

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