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# Standard Deviation stuff

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The following data points are the number of games pitched by each of the Greenbury Goblins' starting pitchers last season.

3,2,4,7

Find the standard deviation of the data set.

Can you please check what I did so far and help me out with the rest?

Thank you!

4

Work:

(3+2+4+7)/4

=16/4

=4

### Difference Thingys:

 -1 -2 0 3

Work:

 3 2 4 7 3 - 4 2 - 4 4 - 4 7 - 4 -1 -2 0 3

Then I'm stuck... 😭😭😭

Would LOVE some help out here... 🙂🙂🙂

$$Tommarvoloriddle$$

Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019

#1
+3

Sorry the edit keeps messing it up...

The first "answer" I put Mean on top of, so the mean is 4

the 2nd "answer" I put Difference things on top of.

The charts are the difference thingys...

But from there I have absolutely NO IDEA what to do...

 😭 😭 😭 😭 😭 😭 😭 😭 😭
Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
#2
+2

3,2,4,7

Find the standard deviation of the data set.

Standard deviation of the sample

$$s^2=\frac{\sum(x_i-\overline x)^2}{n-1}$$

$$n=4\\ \overline x=4$$

$$s^2=\frac{(3-4)^2+(2-4)^2+(4-4)^2+(7-4)^2}{4-1}\\ s^2=\frac{1+4+0+9}{3}\\ s^2=\frac{14}{3}$$

$$s=\sqrt{\frac{14}{3}}\\ s=2.1602469$$

$$s\approx 2.16$$ !

Aug 19, 2019
edited by asinus  Aug 19, 2019
#4
+1

wait- there's a formula?

tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
#3
+2

3,2,4,7

Find the standard deviation of the data set.

Standard deviation of the sample

$$s^2=\frac{\sum (x_i-\overline x)^2}{n-1}$$

$$n=4\\ \overline x=\frac{3+2+4+7}{4}\\ \overline x=4$$

$$s^2=\frac{(3-4)^2+(2-4)^2+(4-4)^2+(7-4)^2}{4-1}\\ s^2=\frac{1+4+0+9}{3}\\ s^2=\frac{14}{3}\\ s=\sqrt{\frac{14}{3}}=2.1602469$$

$$s\approx 2.16$$

Standard deviation of the population

$$s^2=\frac{\sum (x_i-\overline x)^2}{n}$$

$$s^2=\frac{(3-4)^2+(2-4)^2+(4-4)^2+(7-4)^2}{4}\\ s^2=\frac{1+4+0+9}{4}\\ s^2=\frac{14}{4}\\ s=\sqrt{\frac{14}{4}}=1.87083$$

$$s\approx 1.87$$ !

Aug 19, 2019
edited by asinus  Aug 19, 2019
#6
+4

I didn't know there was a formula...

But I think your way is the better way, as my math textbook is just teaching you steps you can use but are crazily bulky.

tommarvoloriddle  Aug 19, 2019
#5
+4

I learned it using steps like above but you would continue it like this(found my math textbook yay)

:

 x mean x-mean (x-mean)^2 3 4 -1 1 2 4 -2 4 4 4 0 0 7 4 3 9 I knew this I knew this I knew this I figured it out right now

Then you have to find the mean of the last column

(1+4+0+9)/4

14/4

7/2

then square root that to get

sqrt(7/2)

which is around 1.87

(Textbook way, no formula...)

I think This problem was categorized terribly as it accepts the population answer.

Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019
edited by tommarvoloriddle  Aug 19, 2019