Sage-Tips

Can two different distributions have the same mean but different standard deviation?

Two data sets can have the same mean and Standard Deviation but have different values of data points. For example if one data set is a linear multiple of the other, or a mirror of the other with some random noise, they could have same mean and Standard Deviation.

Is it possible that two datasets can have the same mean but different variances?

Yes, two sets of data have the same mean, but not the same variance. Two data sets may have the same mean, but different variances.

Can two data sets have the same standard deviation?

1 Expert Answer They could have different means, the data could be distributed differently even though the standard deviations compute to the same value because of differing data values.

Is it possible for two or more sets of values to have the same standard deviation and variance?

It is possible for two or more sets of values to have the same standard deviation and variance. The range is equal to the square of the variance. The variance is equal to the square of standard deviation. The standard deviation is equal to the square of the variance.

Do two distributions have the same mean?

Nevertheless, comparing means and standard deviations do not guarantee that the distributions are similar — you may have two distributions with the same mean and standard deviation that, e.g., have different skewness and/or kurtosis.

Could two sample groups have the same mean but different ranges explain?

a. Could two samples have the same mean but different ranges? Yes, the mean does not reflect the distribution of numbers.

Is it possible to create two data sets with similar standard deviations but different means provide your example?

Yes, absolutely! Both the median and mean are measures of “central tendency”, whereas the standard deviation measures spread around this measure. So yes, it’s definitely possible to have the same mean/median but completely different spreads around this.

What happens if the standard deviation is the same?

All of the individual data values would be clumped together at a single value. In this situation, when all of our data values are the same, there would be no variation whatsoever. Intuitively it makes sense that the standard deviation of such a data set would be zero.

Are two distributions significantly different?

In general, in more qualitative terms: If the Z-statistic is less than 2, the two samples are the same. If the Z-statistic is between 2.0 and 2.5, the two samples are marginally different. If the Z-statistic is between 2.5 and 3.0, the two samples are significantly different.

How do you know if two distributions are the same?

The Kolmogorov-Smirnov test tests whether two arbitrary distributions are the same. It can be used to compare two empirical data distributions, or to compare one empirical data distribution to any reference distribution. It’s based on comparing two cumulative distribution functions (CDFs).

Can two normal distributions have the same mean but different standard deviation?

Yes. In the trivial case, take any two normal distributions which aren’t equal to each other. The mean and/or the standard deviations won’t be equal. To find two normals with different mean but same standard deviation, simply fix the standard deviation and select two non-identical means.

What is the standard deviation in statistics?

Standard deviation is a scale parameter – it measures the dispersion of the data. Here is a data set with mean and median both equal to zero: -2,-1,0,1,2. And here is another with the same mean and median but larger standard deviation: -20,-10,0,10,20.

What is the best way to compare standard deviation between two variables?

A direct reply to your last question is: you can use an F-test to compare variances (the square of the standard deviations). Better versions of this test are the Levene’s test or the Bartlett’s test. However, there are other approaches that may be more accurate.

Is it possible to have the same mean/median but completely different spreads?

Both the median and mean are measures of “central tendency”, whereas the standard deviation measures spread around this measure. So yes, it’s definitely possible to have the same mean/median but completely different spreads around this. For simplicity, we’ll use some symmetrical datasets, so their mean and median is exactly the same.

https://www.youtube.com/watch?v=x_-7hPb11ds