Statistics are cute... 3:)

First, we need to get the mean, and for that we need the sum of all the numbers in the 2013th row . We can calculate it like the sum of an AP with difference 2.

We can calculate the last term of each row by adding the number of the row with the numbers of all the previous rows and then multiply that by 2 and substract 1. In example: To calculate the last term of the 5th row : $2(1+2+3+4+5)-1=29$

So, to calculate the last term of the 2013th row : $2013(2+(2013-1))-1=4,054,181$

Knowing the last term we can calculate the 1st term, trying to solve this problem i note that the last term could be calculated by adding to the first term of any $n$ row 2 times the number of that $n$ row and then substract 2. So the first term can be calculated by substracting to the last term, 2 times the number of the row and add 2. So, the first term is:

$4,054,181-2(2013)+2=4,050,157$

Now, to calculate the sum of the 2013 terms :

$\dfrac{2013(2(4,050,157)+(2013-1)\times 2}{2}=8,157,016,197$

Now:

$Mean=\dfrac{8,157,016,197}{2013}=\boxed{4,052,169}$

For the median we need to know the $1007th$ term so we need the formula to calculate the $n$ term of an AP:

$Median=1007\times2+(4,050,157-2)=\boxed{4,052,169}$

Other way to calculate the median is, adding the first term and last term and then divide by 2, because the the term of an AP that it's in the center is $2$ times the sum of the terms that are in the extremes:

$\dfrac{4,050,157+4,054,181}{2}=\boxed{4,052,169}$ .

Now the range, like we have the first and last terms, it's easy to calculate:

$Range=4,054,181-4,050,157=\boxed{4,024}$

Finally:

$\dfrac{4,024+2(4,052,169)}{2}=\boxed{4,054,181}$

First, get the mean...

The mean is just the square of the row #.

Mean = 2013^2 = 4052169

2nd, median = mean = 4052169

3rd, the range.

The range is just, the row # - 1 multiplied by 2...

Range = (2013 - 1)*2 = 4024

Finally,

(mean + median + range)/2 = (4052169+4052169+4024)/2 = 4052169+2012 = 4054181

Final answer: 4054181.

First you should list the mean of each of row: 1 4 16 25 36 ... etc. You will notice that the mean for each row is simply the row number squared. So, the mean of row 2013 would be 2013^2 or 4,052,169.

Next you do the same for the median: 1 4 16 25 36 ...etc. You again notice that the patter is identical to the pattern found for the mean, so you will just use the same calculation that you used prior. 2013^2 or 4,054,169.

Then you do the same for the range: 0 2 4 6 8 10 ...etc. However, now you see that there is a different pattern here. The pattern here is simply taking the row number, subtracting it by one and then multiplying it by two. So, in order to find our range for row 2013 all you simply need to do is calculate (2013-1)*2 which is equal to 4,024.

Finally you take your numbers and input them into the equation that was given. So, your answer would be (4,052,169+4,052,169+4,024)/2 which is equal to 4,054,181.