# For these numbers: 2,2,0,5,1,4,1,3,0,0,1,4,4,0,1,4,3,4,2, what is the (a) mean, (b) median, (c) variance and (d) standard deviation?

Sep 27, 2017

Mean $= \frac{41}{19} \approx 2.158$

Median $= 2$
Variance $= \frac{960}{361} \approx 2.659$
Standard Deviation $= \sqrt{\frac{960}{361}} \approx 1.631$

#### Explanation:

Quick note: I will deal with fractions until the end, because if I simplify my results too early then the results will be inaccurate.

The median is the middle number in an ordered data set. This data set has an odd number of elements, which means the median will be one of the elements. After I put the set in order, I simply count how many values there are (19), see that the number below 19 is 18 which divided by 2 equals 9, count 9 numbers, and the number next to that is the middle number. This happens to be 2.

The mean is the sum of all the values divided by the number of values. It looks like this:
$\frac{0 + 0 + 0 + 0 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 5}{19}$
$= \frac{41}{19} \approx 2.158$

From here, if you want an in-depth explanation of how to do this, see this answer.

To find the variance I find the average of the squared distances from the mean, which ends up looking like this:
=(960/19) ÷ 19
$= \frac{960}{361} \approx 2.659$

To find the standard deviation I simply find the square root of the variance, which looks like this:
$\sqrt{\frac{960}{361}} \approx 1.631$

I hope I helped!