Question

What is the standard deviation of the data set?

9 14 23 15 6 18 27



≈6.8


≈7.4


≈2.6


≈3.0

Answer 1

First, add up all the numbers,
9+14+23+15+6+18+27=112

Answer 2

Next, divide the total by the amount of values. 112/7=16

Answer 3

Now, we have our mean: 16. The standard deviation is the average distance from the mean.

Answer 4

So now we have have to add up all the differences squared, then find the square root.

Answer 5

In other words, the square root of
((9-16)^2)+((14-16)^2)+((23-16)^2)+((15-16)^2)+((6-16)^2)+((18-16)^2)+((27-16)^2)

Answer 6

Phew! Anyway, I'll tackle this long equation for you. The answer is 328.

Answer 7

Now we have to find the average of all those.

Answer 8

That's going to be 328/7

Answer 9

Which is 46.857142857...

Answer 10

Take the square root of that and we have our answer.

Answer 11

@malcolmmcswain Nice job at solving this! ;)

Answer 12

@Ghostgate Thanks so much! I'm exhausted! :P

Answer 13

No problem, I'm just appreciating how you went through step by step to solve it.

Answer 14

Our answer is 6.845227743... which is approximately 6.8

Answer 15

HOORAY! We're done.

Answer 16

@malcolmmcswain Again, good job! ;)