Standard Deviation (1 Viewer)

[i.am.ashlee]

Can somebody please explain standard deviaton to me?
I know how to work it out, but i have no idea what it is.

For example, i am stuck on the question
"In a normally distributed set of scores, the mean is 55 and the standard deviation is 15. Approximately what percentage of scores lie between 25 and 70?"

I dont even know where to start

 

[tanjin]

Isn't there an explanation of this in your text book?

http://en.wikipedia.org/wiki/Standard_deviation

LOL wikipedia...seriously its detailed enough

 

[LatK7]

Is it 81.5%?

 

[tanjin]

Is it 81.5%?

She's stuck on the question so she wouldnt know the answer yet...

 

[LatK7]

Maybe you know the answer

 

[yosemite sam]

wikipedia is heaps hard to understand....standard deviation is basically just how evenly the scores are distributed around the mean. if the z-score is +1, the score is in the set of scores that are one standard deviation above the mean. how the deviate around the mean. yes...does that help?

 

[Sh4DoW]

This is hard to explain!

Basically, you draw the bell curve. The full curve represents 100% of scores and a half curve represents 50% of scores. You're really going to have to remember what percentage of scores account for each deviation from the mean for the exam!

To answer your question though. If the mean is 55, and the sd is 15, then:

70

= 70-55
15

+1sd from the mean = 34%

25

= 25-55
15

-2sd from the mean = 34% + 13.5%

Therefore the percentage of scores between 25 and 70
= 34% + 34% + 13.5%
= 81.5%

 

[tanjin]

Maybe you know the answer

LOL....






NO
My mind prevents me from working well with numbers.

 

[LatK7]

I was correct. Huzzah!

 

[tanjin]

I was correct. Huzzah!

 

[PC]

In a normally distributed set of scores, the mean is 55 and the standard deviation is 15. Approximately what percentage of scores lie between 25 and 70?

I do these a different way. Stuff the curve, who needs it!

Start all these questions by drawing up a number line with 7 marks on it (-3s, -2s, -1s, mean, 1s, 2s, 3s).

Then work out the numbers that correspond.

For this question, mean is 55 and sd is 15.

So:
-3s -2s -1s x 1s 2s 3s
|----|----|----|----|----|----|
10 25 40 55 70 85 100

Now 25 is 2 sd below the mean, so 1/2 x 95% = 47.5%
And 70 is 1 sd above the mean, so 1/2 x 68% = 34%

So marks between 25 and 70 is 47.5% + 34% = 81.5% of all scores.

 

[Sh4DoW]

I do these a different way. Stuff the curve, who needs it!

Start all these questions by drawing up a number line with 7 marks on it (-3s, -2s, -1s, mean, 1s, 2s, 3s).

Then work out the numbers that correspond.

For this question, mean is 55 and sd is 15.

So:
-3s -2s -1s x 1s 2s 3s
|----|----|----|----|----|----|
10 25 40 55 70 85 100

Now 25 is 2 sd below the mean, so 1/2 x 95% = 47.5%
And 70 is 1 sd above the mean, so 1/2 x 68% = 34%

So marks between 25 and 70 is 47.5% + 34% = 81.5% of all scores.

that's the same as drawing a bell curve, except without the curve. i suggested that because they didn't know where to start, and with the percentages for each sd from the mean, that's the easiest way to learn.