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The variance measures how far each number in the set is from the mean

I have 151190 records of a table. and i have to analyze the data on SPSS. after the analysis i have some results. Mean=74617.92 with standard error=871.744, Median=94118, variance= 1393725134, Standard Deviation= 37332.628, Minimum= 1353, Maximum= 95085, Skewness= -.007, Kurtosis= -1.31. I cannot understand the relation why there is a huge gape between mean and variance.

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  • $\begingroup$ The variance is in squared units, which sometimes makes variances very large (or very small) numerically. However, you can have data with a small mean and a large standard deviation. Standard deviation is a measure of dispersion that has the same units as the mean. // Example: Maybe stock values are the same now as several months ago, but they have fluctuated widely + and - from day to day over the same period. // When I took a sample of size 100,000 from NORM($\mu$=0,$\sigma$=100) then I got sample mean $\bar X = -0.061,$ SD $S = 99.78$ and variance $S^2 = 9955.29.$ I guess all is OK. $\endgroup$
    – BruceET
    Oct 22, 2018 at 7:14

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When looking at how the data is spread, you should look at the standard deviation which has the same unit as the mean. The variance is the standard deviation squared, it thus doesn't give you a clear idea of the distribution of the data. If you have a big standard deviation means that your data has a big range, and in your case is skewed to the left since your means lies far to the left of the median

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  • $\begingroup$ In real i don't have the clear understanding of variance and standard deviation. and how these will help me to analyze the data. $\endgroup$ Oct 22, 2018 at 6:56
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Perhaps somewhere you learned about the Coefficient of Variation (CV). You can look that up on the internet and see if that is what you are thinking of and why you might want to look at it.

In general, people look at measures of center (like the mean, mode, and.or median) and spread (the standard deviation, range, etc.) to help understand more about the distribution of a variable. When we measure something we want to describe and perhaps even make inferences about using some method of analysis, the shape of the distribution helps us figure out what statistical methods might be useful and which less useful.

For example, see https://www.quora.com/What-does-it-mean-when-the-standard-deviation-is-higher-than-the-mean-What-does-that-tell-you-about-the-data

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