How can two samples have the same mean but different standard deviations?

How can two samples have the same mean but different standard deviations?

If two samples have the same mean, then this implies that the two values in the two samples are centered about the same value. 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.

What has the same mean and standard deviation?

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.

Is it possible that two datasets can have the same mean but different variances give an artificial example to justify your answer?

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.

Could 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.

When do two samples have the same mean, standard deviation?

Perhaps the easiest case is to take an asymmetric sample of size N = 3 and flip it around its mean ( 2, 3 and 7 have a mean of 4; if you take a new sample of 6, 5 and 1, respectively, it has the same mean and the same magnitude of deviations from the mean as the original sample, so it will have the same variance and hence standard deviation).

What does sample mean stand for in statistics?

The sample mean is a random variable; as such it is written , and stands for individual values it takes. As a random variable the sample mean has a probability distribution, a mean , and a standard deviation .

Is the mean of a sample a random variable?

In actual practice we would typically take just one sample. Imagine however that we take sample after sample, all of the same size , and compute the sample mean each time. The sample mean is a random variable: it varies from sample to sample in a way that cannot be predicted with certainty.

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

If you also have (approximately) normally distributed data, then it means that the variation (spread) in the two data sets is the same. This is useful in many analytic contexts, in particular comparisons of means. For some other distributions you can also draw conclusions, but a fact like that in isolation is not informative.