• July 1, 2022

### Can You Have The Same Mean And Different Standard Deviation?

• Can you have the same mean and different standard deviation? The mean is a measure of the center of some sample, while the standard deviation is a measure of variation of some sample. However, this does not mean that the data values in the samples vary the same amount about this center and thus the standard deviations can be different.

## Can two data sets have the same mean and standard deviations?

No. Many data sets can yield the same mean, SD and n. In the graph above, the three data sets on the left of each graph all share the same mean, SD and n.

## 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 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.

## How do you compare two different standard deviations?

Comparison of two standard deviations is performed by means of the F-test. In this test, the ratio of two variances is calculated. If the two variances are not significantly different, their ratio will be close to 1.

## Related faq for Can You Have The Same Mean And Different Standard Deviation?

### 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.

### What does it mean to have a different standard deviation?

The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean. 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.

### What do similar standard deviations mean?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

### What is the standard deviation of a data with equal value of entries?

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 is one standard deviation away from the mean?

For an approximately normal data set, the values within one standard deviation of the mean account for about 68% of the set; while within two standard deviations account for about 95%; and within three standard deviations account for about 99.7%.

### When standard deviation increases what happens to your standard error?

Standard error increases when standard deviation, i.e. the variance of the population, increases. Standard error decreases when sample size increases – as the sample size gets closer to the true size of the population, the sample means cluster more and more around the true population mean.

### Is standard deviation useful when comparing sets of data with the same mean but a different range?

Remember, the smaller the standard deviation, the more closely the data cluster about the mean. This information is useful in comparison to other datasets. 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.

### What happens if two data sets have the same range?

Your friend says that when two data sets have the same range, you can assume the data sets have the same standard deviation, because both range and standard deviation are measures of variation.

### Is it possible for the standard deviation to be greater than the mean?

Yes, the standard deviation can be greater than the mean and whether it is a good or a bad thing, depends on the sort of data being looked at (or investigated). It is not an abnormal. As a matter of fact, a standardized normal distribution data has a mean value of 0 and SD of 1.

### What does it mean when two groups have the same mean?

Two groups of means are equal means that both are equal and no need to apply any statistical test.

### How do you compare two standard distributions?

The simplest way to compare two distributions is via the Z-test. The error in the mean is calculated by dividing the dispersion by the square root of the number of data points. In the above diagram, there is some population mean that is the true intrinsic mean value for that population.

### How do you compare two means?

• Independent Samples T-Test.
• One sample T-Test.
• Paired Samples T-Test.
• One way Analysis of Variance (ANOVA).

• ### How does mean deviation differ from standard deviation?

If you average the absolute value of sample deviations from the mean, you get the mean or average deviation. If you instead square the deviations, the average of the squares is the variance, and the square root of the variance is the standard deviation.

### What is the difference between standard deviation and standard deviation of the mean?

The standard deviation (SD) measures the amount of variability, or dispersion, from the individual data values to the mean, while the standard error of the mean (SEM) measures how far the sample mean (average) of the data is likely to be from the true population mean. The SEM is always smaller than the SD.

### What is the relation between mean deviation and standard deviation?

In a discrete series (when all values are not same), the relationship between mean deviation (M.D) about mean and standard deviation (S.D) is. (a) M. D=S.

### What is the standard deviation if all of the sample values are same?

If all of the values in the sample are identical, the sample standard deviation will be zero.

### What does it mean when a data set has a standard deviation equal to zero?

When the standard deviation is zero, there is no spread; that is, the all the data values are equal to each other. The standard deviation is small when the data are all concentrated close to the mean, and is larger when the data values show more variation from the mean.