[Math] I am getting a number below zero when caluclating out two standard deviations from the mean. Is this ok

statistics

I am not a math wizard, so please keep your response simple enough. I need to complete a statistics screening exam for a methods course later on today and I am hung up on one topic that came up during the practice test. The data set I got was in reference to the number of homicides that have occurred in a number of cities. This range of the data is 0-5. When I am putting together confidence intervals and calculating out as much as two standard deviations from the mean I am getting low values that are negative. Obviously you can not have a negative number of homicides. When calculating the confidence intervals and out to two standard deviations from the mean should present the low value at ZERO or should I actually present the negative number? For example, if a 95% CI caused the calculation to be -1.5 to 3, would I present that or would I present 0 to 3? Thanks.

Best Answer

This is certainly fine. What you tell me, 95% of the data is between -1.5 and 3. That is a correct statement. But it is even better, 95% of the data is between 0 and 3 for the precise reason that you indicate.

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[Math] Calculating mean and standard deviation of very large sample sizes

Posting as an answer in response to comments.

Here's a way to compute the mean and standard deviation in one pass over the file. (Pseudocode.)

n = r1 = r2 = 0;
while (more_samples()) {
    s = next_sample();
    n += 1;
    r1 += s;
    r2 += s*s;
}
mean = r1 / n;
stddev = sqrt(r2/n - (mean * mean));

Essentially, you keep a running total of the sum of the samples and the sum of their squares. This lets you easily compute the standard deviation at the end.

[Math] Is it possible to calculate the mean and standard deviation from a median and quartiles

It's mathematically impossible to deduce mean or standard deviation from median/quartiles, because medians and quartiles discard most of the data on which the mean and standard deviation are based.

Example:

data   frequency  
   0       50      
 1.4        4     
   2       50

That has a mean of 1.0 and standard deviation of 0.9. (I'm using 2 significant figures so I don't have to go into population versus sample standard deviation.)

data     frequency    
   0       30        
 1.4       44        
   2       30

That data also has the median and quartiles the same as in your example, but now the mean is 1.2 and the standard deviation is 0.8.

data     frequency        
   0       30        
 1.4        3        
   2       70        
10000000    1

Now I've changed my maximum without changing the median or quartiles, you can see even more clearly how the median and quartiles exclude extreme data, because the mean is now 96000 and the standard deviation is 98000 (still 2 sig.fig.).

Best Answer

Related Solutions

[Math] Calculating mean and standard deviation of very large sample sizes

[Math] Is it possible to calculate the mean and standard deviation from a median and quartiles

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