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.

Can you have the same standard deviation but different means?

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. The standard deviation alone doesn’t tell you much of anything.

Can two sets of data have the same variance but different means?

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.

What happens if two data sets have the same range?

1) a) The distance from the smallest to largest data in both sets will be the same.

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).

Can you compare standard deviation between two data sets?

Most of the results in data set 2 are close to the mean, whereas the results in data set 1 are further from the mean in comparison. This suggests that the standard deviation is smaller in data set 2 than data set 1….Standard deviation.

x	X − X ¯	( X − X ¯ ) 2
50	50 − 55 = − 5	( − 5 ) 2 = 25
72	72 − 55 = 17	( 17 ) 2 = 289
	Total	628

Can range and standard deviation be equal?

So the best case (two data points 0 and 1) yields a standard deviation of 0.7071 which is more than 50\% of the range. This gives you a standard deviation of 0 and a range of 0. So it’s possible to get a standard deviation equal to the range, but only for this one special case.

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.

Could two sample groups 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.

What does it mean to have a different standard deviation?

The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.

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

Can two different data sets have the exact same mean and median but have very different standard deviations? Yes, absolutely! Both the median and mean are measures of “central tendency”, whereas the standard deviation measures spread around this measure.

How to find the mean of the second data set?

The mean of the second data set = c + mean of the first data set. But range and standard deviation of both data sets will be the same. SRIPADASRIKAR .

What is the difference between the first and second data set?

2 Answers 2. The two data sets have different dispersion as it is expressed by the standard deviation. In the first data set, the observations are located more closely around the mean (50) compared to the second data set, where they are more dispersed.

How do the two data sets have different dispersion?

The two data sets have different dispersion as it is expressed by the standard deviation. In the first data set, the observations are located more closely around the mean (50) compared to the second data set, where they are more dispersed.