# statistics question

can someone plz help me out with this statistical question? if i take the 75th percentile and the 25th percentile of my data set, i get a much wider range (9.9, 21.15) than if i take my sample mean and move it up and down by 1 standard deviation: (15.98, 16). does anyone know why this would be? doesnt the 75th-25th percentile kind of represent about 50% of my data, while +/- 1 standard deviation represents about 68% of my data? any ideas where im going wrong? thanks!

68% rule works for normal distribution only, for more general case check out Chebyshev’s inequality: http://en.wikipedia.org/wiki/Chebyshev’s_inequality

maratikus Wrote: ------------------------------------------------------- > 68% rule works for normal distribution only, for > more general case check out Chebyshev’s > inequality: > http://en.wikipedia.org/wiki/Chebyshev’s_inequalit > y agreed. Would that mean the distribution is meso-kurtotic and thin tailed compared to normal? I always mess this stuff up.

You calculated something incorrectly if your standard deviation is .01 (15.99 ±.01) and your 25th and 75th percentiles are 9.9 and 21.15.

thanks guys! wutsaCFA, this is coming right out of SPSS’s output. the sample size is very large, n=6946, maybe that has something to do with it? Descriptive Statistics N Minimum Maximum Mean Std. Deviation lrate 6946 .00 .75 .1599 .10016 Valid N (listwise) 6946 Statistics lrate N Valid 6946 Missing 0 Percentiles 25 .0919 50 .1462 75 .2115

1 Standard Deviation in either direction of the mean would be (.0598, .2601) not (.1598, .1600). This is bigger than the difference between the 25th and 75th percentiles (.0919, .2115), so the issue you are describing doesn’t exist. You just miscalculated the mean + stdev.

Uh, I think the problem is that the mean is 0.1599, not 15.99. Odd stuff tends to happen when you arbitrarily multiply things by 100.