Question

Find the standard deviation of first 13 natural numbers​

Answer 1

hey mate⚡️

please mark me as brainliest

I'm going to assume that your definition of Natural numbers starts a 1, so the first 13 are the numbers from 1 to 13.

Also I'm assuming that you are getting the population standard deviation which means we will use N instead of N-1 later on.

So for standard deviation we will first need the mean (also called the average). For that we need to sum all the numbers and divide by how many numbers we added up (in this case 13).

There is a nice trick for summing up numbers starting at 1 which is

n+%2A+%28n%2B1%29+%2F+2 which gives us 91 for n=13. When we divide by n to get the average, we get 7.

Standard deviation is defined as the square root of the sum of the squared errors divided by n (or sometimes n-1, check with your teacher for what they want).

The "error" means the difference from the mean. So for example the error for the first number 1 is (7-1 = 6). We square this to get 36.

We do this for each number and add them up.

1) 7-1 = 6, 6*2 = 36

2) 7-2 = 5, 5^2 = 25

3) ... 16

4) ... 9

5) ... 4

6) ... 1

7) ... 0

8) ... 1

9) ... 4

10) ... 9

11) ... 16

12) ... 25

13) ... 36

Summing those we get 182. We divide 182 by 13 since we have 13 numbers = 14. Lastly we take the square root to get 3.7416

Answer 2

Answer:

91 for n=13.

Step-by-step explanation:

So for standard deviation we will first need the mean (also called the average). For that we need to sum all the numbers and divide by how many numbers we added up (in this case 13). which gives us 91 for n=13.