# A little help understanding standard deviation & variance

1. Jan 3, 2012

### tomtomtom1

Hello all

This is not homework, i work in engineering.

I have some data in a table, there are 3 columns and 5 rows.

The data relates to how high or low one rail is to the other.

The data was collected across 3 days. At each 7m intervals the height of the right hand rail was measured against the left hand rail.

The objective was to determine if the rails were moving up or down from each other and then to calculate if that movement was severe.

After calculating the mean, variance and SD, I can say that;

at each position there was 2 x data points within 2 x SD of the mean and 1 x data point within 1 SD of the mean and 0 x data points within 3 SD of the mean.

But what does this mean, how do you interpret the data, what is the data telling me in context of my example???

I know that if all of my data points was within 1 SD of the mean then would that indicate that there is little movement between the rails at each position.

After looking at the data & the SDs would you say that between 0 – 28m there is lots of movement or little movement & how can you quantify this interms of a percentage for exameple.

Attached is the data I am using.

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2. Jan 3, 2012

### D H

Staff Emeritus
On the face of it, this statement makes no sense.

If there is any way to post your data as anything but a .xls file you might get more views. I for one do not touch unknown Microsoft attachments. There's just too much chance of an infection. I don't know whether you are malicious, and assuming you aren't, I don't know how vigilant you are with respect to viruses.

3. Jan 3, 2012

### tomtomtom1

Attached is a PDF file of the data.

As for the statement "...at each position there was 2 x data points within 2 x SD of the mean and 1 x data point within 1 SD of the mean and 0 x data points within 3 SD of the mean.'

You see what i mean when you see the data.

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4. Jan 3, 2012

### D H

Staff Emeritus
What do those population samples represent? For example, what is the meaning of the value 2.9 at a position of 0 meters on day #3, versus the meaning of the value of 1.100 at a position of 28 meters on day #1? (And why 1.100 versus 2.9?)

What exactly are you measuring here?

5. Jan 3, 2012

### tomtomtom1

The population sample represents differences in height between the left hand rail and the right hand rail.

So if you imagine yourself standing in the middle of a railway track. There are two rails one on your left and the other to your right.

Starting at some postion, lets say 0m, on Day 1; at that cross section of the track the left hand rail is higher then the right hand rail by 1.900 units.

You then walk 7m from where you started; you then measure the height differences at that cross section, in this case the left hand rail is higher then the right by 1.800 units.

You continue this process until you get to postion 28m.

On day 2, you do exactly the same thing, but you measure the height differences at exactly the same postions i.e at 0m, 7m .... 28m.

Finally on day 3, you do the same thing as you did in day 2.

6. Jan 3, 2012

### D H

Staff Emeritus
OK.

By computing statistics across days you are losing the very statistic you want to see, which is whether the tracks are shifting over time. It looks to me like what you want is a regression or an analysis of variance. Excel has some pretty nice regression and ANOVA tools.

Here's a brief description of ANOVA: http://www.biology.ed.ac.uk/research/groups/jdeacon/statistics/tress8.html. This page contains a worked example that is very similar in form to yours. It appears to me that position is not statistically significant but day number most definitely is. In other words, the tracks are shifting over time.

Last edited: Jan 3, 2012