How can median be greater than mean

In fact, the mean will be lower than the median in any distribution where the values "fall off", or decrease from the middle value faster than they increase from the middle value. How can a median be greater than the mean? Jan 29, Explanation: The median of a set of numbers is the value that is in the middle In a set with an odd number of values, it's the middle value. Related questions How do the different measures of center compare? What is the difference between the sample mean and the population mean?

How do you find the median of a set of values when there is an even number of values? What is the median for the following data set: 10 8 16 2. What is the median for the following data set: 10 8 16 2 However, the study group often also includes patients who have been suffering from the disease for many years.

If we calculate the mean of the individual time spans since disease onset, such large values have an enormous impact, making the mean larger than the actual distribution of data would suggest.

Therefore, here the median gives a more realistic picture of the data. If they are not too different , use the mean for discussion of the data, because almost everybody is familiar with it.

If both measures are considerably different, this indicates that the data are skewed i. Stuck in the middle — mean vs. As an example, let us consider the following five measurements of systolic blood pressure mmHg : , , , , The median is defined as the value which is located in the middle, i.

Mean vs. So which one should we use? The best strategy is to calculate both measures. Sign up now! More information. By Dr. About the Author: Dr. The mean is [latex]6. Notice that the mean is less than the median, and they are both less than the mode. The mean and the median both reflect the skewing, but the mean reflects it more so. It is skewed to the right. The mean is [latex]7. Of the three statistics, the mean is the largest, while the mode is the smallest.

Again, the mean reflects the skewing the most. To summarize, generally if the distribution of data is skewed to the left, the mean is less than the median, which is often less than the mode. If the distribution of data is skewed to the right, the mode is often less than the median, which is less than the mean. Skewness and symmetry become important when we discuss probability distributions in later chapters.

Here is a video that summarizes how the mean, median and mode can help us describe the skewness of a dataset. Statistics are used to compare and sometimes identify authors.

The following lists shows a simple random sample that compares the letter counts for three authors.