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October 21, 2025, 05:09:32 pm
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Author Topic: Standard deviation  (Read 2993 times)  Share 

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#J.Procrastinator

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Standard deviation
« on: October 10, 2013, 04:16:41 pm »
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Hi guys!

How do we find the standard deviation from just a histogram? I came across this question in a kilbaha exam and had absolutely no idea how to find it  :-\. Thanks!!


« Last Edit: October 11, 2013, 03:54:52 pm by #J.Procrastinator »
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Damoz.G

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Re: Standard devation
« Reply #1 on: October 10, 2013, 04:49:02 pm »
+1
Quote from: #J.Procrastinator on October 10, 2013, 04:16:41 pm
Hi guys!

How do we find the standard deviation from just a histogram? I came across this question in a kilbaha exam and had absolutely no idea how to find it  :-\. Thanks!!




You have to manually enter the Data into a Lists and Spreadsheets document on your CAS to find it.

An alternative, is to use the formula, but you are more likely going to make a mistake, and it will take longer. Safer to enter the data onto your CAS. :)
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#J.Procrastinator

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Re: Standard devation
« Reply #2 on: October 10, 2013, 05:11:33 pm »
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Ah alrighty, thanks :)

What if they just provide us with a boxplot? Is there any way of figuring the standard deviation from that?
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Damoz.G

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Re: Standard devation
« Reply #3 on: October 10, 2013, 05:47:45 pm »
+1
Quote from: #J.Procrastinator on October 10, 2013, 05:11:33 pm
Ah alrighty, thanks :)

What if they just provide us with a boxplot? Is there any way of figuring the standard deviation from that?

Can't exactly remember, but you may need to use that big Standard Deviation formula then.

I don't think VCAA would ever get you to go that far though to get the answer though.
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Yacoubb

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Re: Standard devation
« Reply #4 on: October 10, 2013, 11:57:41 pm »
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Range divided by 6. You typically get a question like this for MC.

If the data distribution is approximately symmetric (with no extreme values or outliers), 99.7%, which is very close to 100% of the data, lies within 3 standard deviations either side of the mean. Hence, you find the range and divide it by 6 to get an approximate standard deviation.
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#J.Procrastinator

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Re: Standard devation
« Reply #5 on: October 11, 2013, 01:15:14 am »
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Thank you! Btw, we'll most likely not have to use the Standard Deviation and variance formula right? I've done about 40 practice exams and none have asked me to use it.

Yeah, I've done a couple MC questions having me compare the standard deviation, and I was unsure about how to approach it.
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Damoz.G

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Re: Standard devation
« Reply #6 on: October 11, 2013, 07:37:41 am »
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Quote from: #J.Procrastinator on October 11, 2013, 01:15:14 am
Thank you! Btw, we'll most likely not have to use the Standard Deviation and variance formula right? I've done about 40 practice exams and none have asked me to use it.

Yeah, I've done a couple MC questions having me compare the standard deviation, and I was unsure about how to approach it.

From memory, I don't think you are expected to calculate Standard Deviation and Variance using the formulas. None of the Practice Exams when I did Further last year, required me to calculate it where I couldn't use a Lists and Spreadsheets Document.

You could always use the Z Score formula as well, if you have the other 3 bits of information, and then solve for the unknown. :)
« Last Edit: October 11, 2013, 07:40:09 am by Damoz »
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abcdqdxD

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Re: Standard devation
« Reply #7 on: October 11, 2013, 10:43:26 am »
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Quote from: Yacoubb on October 10, 2013, 11:57:41 pm
Range divided by 6. You typically get a question like this for MC.

If the data distribution is approximately symmetric (with no extreme values or outliers), 99.7%, which is very close to 100% of the data, lies within 3 standard deviations either side of the mean. Hence, you find the range and divide it by 6 to get an approximate standard deviation.

I thought it was range/4?
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Zealous

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Re: Standard devation
« Reply #8 on: October 11, 2013, 02:42:00 pm »
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Quote from: abcdqdxD on October 11, 2013, 10:43:26 am
I thought it was range/4?
3 standard deviations on both sides of the mean, so therefore 6 total standard deviations will cover 99.7% of the data.
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Stick

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Re: Standard deviation
« Reply #9 on: October 11, 2013, 03:52:22 pm »
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Quote from: abcdqdxD on October 11, 2013, 10:43:26 am
I thought it was range/4?

This came up last year. I think it was an error in a publication.
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WeaponX

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Re: Standard deviation
« Reply #10 on: October 13, 2013, 09:17:14 pm »
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From what I've heard, when they want you to estimate the standard deviation from just data, it is range/4. However, if they give you the bell curve, then it is range/6. As to why, I have no clue.
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Yacoubb

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Re: Standard deviation
« Reply #11 on: October 13, 2013, 09:57:58 pm »
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Quote from: WeaponX on October 13, 2013, 09:17:14 pm
From what I've heard, when they want you to estimate the standard deviation from just data, it is range/4. However, if they give you the bell curve, then it is range/6. As to why, I have no clue.

If you were given the data, you would probably be asked to find the actual standard deviation, not the estimate. Therefore, you'd plug your data values into your calculator and get your standard deviation. However, if you were given a boxplot, histogram, stem and leaf-plot even, considering they are approximately symmetric with no outliers or extreme values that can distort the value of the mean, you would just calculate range/6. This would give you above 99.7% of the data, which is very close to all 100% of the data values in your distribution.
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