To compute the mean, you simply have to sum all the elments in the data set and the divide the sum by the number of elements:
To compute the variance, we first need to compute the distance of each element from the mean. To do so, we build a "parallel" dataset, given by the difference of every value and the mean:
Now we need those difference squared:
The variance is the mean of this new vector, so
Finally, the standard deviation is simply the square root of the variance, so you have
Answer:
12 minutes
Step-by-step explanation:
Since it takes 4 minutes to fill the bathtub with both taps on and stopper is in then for each minute the 2 taps can fill up to a quarter (1/4) of the tub:
Similarly, it takes 6 minutes to drain the tub with both taps off and the stopper is out. This means for each minute the stopper can drain one sixth (1/6) of the tub.
Therefore, when both taps are on and the stopper is out, then for each minutes, the amount of water remaining in the tub is the water flowing in minus the water draining out
So for each minute, one twelveth of the tub is filled, for the tub to be completely filled in, it would take 12 minutes