Sage-Tips

Can two data sets have the same range but different standard deviations?

Another sample dataset might have the same mean, 53.5, but with a data range from 45 to 62 and a standard deviation of 3.5. The two datasets have the same mean, 53.5, but very different standard deviations.

What if two datasets have the same mean and standard deviation?

Two data sets can have are very different mean values but have the same standard deviations. Therefore, the amount of variance (aka “noise”) in the two data sets is the same, even though the means differ.

Do data sets with the same mean and standard deviation have the same shape?

Data sets with the same mean and the same standard deviation must have the same shape. The mean is less affected by extreme observations than the median. Chebyshev’s Rule gives us an idea what proportion of the data set will fall within certain bounds, regardless of the shape of the distribution.

When two data sets have the same meaning?

For two data sets with the same mean, the one with the larger standard deviation is the one in which the data is more spread out from the center. Standard deviation is equal to 0 if all values are equal (because all values are then equal to the mean).

What does it mean if two data sets have the same mean?

Hi Moriah, Though the two data sets have the same mean, the second data set has a higher standard deviation. This means that scores in that data set will be more spread out around the mean value of 50 compared to the first data set. If you think of a normal distribution, it will help make the point clear.

Can two samples have the same mean but different ranges?

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

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

Does same range mean same standard deviation?

The smaller your range or standard deviation, the lower and better your variability is for further analysis. The range is useful, but the standard deviation is considered the more reliable and useful measure for statistical analyses. In any case, both are necessary for truly understanding patterns in your data.

How are the IQR and the range of a data set similar in terms of comparing data sets?

Range and interquartile range (IQR) both measure the “spread” in a data set. Looking at spread lets us see how much data varies. Range is a quick way to get an idea of spread. It takes longer to find the IQR, but it sometimes gives us more useful information about spread.