Can two sets of data have the same mean but a different 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.

Which distribution has the same mean and standard deviation?

This comes from operations analysis. Often you have measurement of times, such as time between customers arriving at a store (e.g. Starbucks) or time it takes to process an order (e.g. a cappuccino).

Can two sets of data have the same mean but not the same variance?

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.

When comparing sets of data Why is it important to consider both the mean and the mad?

Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set. Mean absolute deviation helps us get a sense of how “spread out” the values in a data set are.

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.

Can standard deviation and mean be the same?

There is no direct relationship between mean and SD because the mean is simple average of algebraic sum of data whereas the SD is obtained from the average of the square of data. Also SD is obtained by removing mean from the data. Statistically, there is no limit on SD with respect to mean.

Is it possible for two different distributions to have the same mean but differ in their variability?

For example, distributions with the same mean can have different amounts of variability or dispersion. Despite the equal means (the mean score for both quizzes is 7), the scores on Quiz 1 are more packed or clustered around the mean, whilst the scores on Quiz 2 are more spread out.

What does mean and MAD mean in math?

What can we do to find the difference between the mean and each data point?

To find the mean absolute deviation of the data, start by finding the mean of the data set. Find the sum of the data values, and divide the sum by the number of data values. Find the absolute value of the difference between each data value and the mean: |data value – mean|.

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

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. Here below is a graphical example, with different means and the same standard deviations:

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.

Can the mean and standard deviation of the data be manipulated?

So thinking out loud…. the mean and standard deviation are only two of many possible statistical measures of the data. You could manipulate the data so that the mean and standard deviation remain the same. Taking additional measures of skewedness or the median or the mode or etc… would uncover the manipulation.

What do the two data sets have in common?

The two data sets have the same central tendency as it is expressed by the mean 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.