October 13, 2025

How To Calculate Mean And Median In Statistics

Q: What is the difference between mean and median?

The mean averages all values, making it sensitive to extremes, while the median identifies the middle value, resisting outliers and better representing the center in skewed distributions.

Q: When should you use the median over the mean?

Use the median when data contains outliers or is skewed, as it provides a more accurate central tendency; for example, in house prices where a few luxury homes distort the average.

Q: How do you handle missing values when calculating mean or median?

For mean, exclude missing values from the sum and count, or impute them if appropriate. For median, sort the available values and find the middle one, ignoring gaps to maintain positional integrity.

Q: Is the mean always greater than the median in skewed data?

In positively skewed data, the mean is typically greater than the median due to high outliers pulling the average up; conversely, in negatively skewed data, the mean is less than the median, though symmetry yields equality.

Discover the straightforward methods to compute the mean and median, key measures of central tendency used to summarize data sets in statistical analysis.

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Calculating the Mean

The mean, or arithmetic average, is calculated by summing all values in a data set and dividing by the number of values. For a data set with values x1, x2, ..., xn, the formula is mean = (x1 + x2 + ... + xn) / n, where n is the total number of values. This provides a balanced central value sensitive to all data points.

Calculating the Median

The median is the middle value in a data set when arranged in ascending order. For an odd number of observations n, it is the (n+1)/2 th value. For an even number, it is the average of the n/2 th and (n/2 + 1) th values. This measure is robust against extreme values, focusing on the central position.

Practical Example

Consider the data set: 3, 7, 2, 9, 1. First, sort it: 1, 2, 3, 7, 9. The mean is (1+2+3+7+9)/5 = 22/5 = 4.4. The median is the third value, 3. In this case, the mean is influenced by the outlier 9, while the median remains stable at 3.

Importance and Applications

Mean and median are fundamental in descriptive statistics for summarizing data distributions. The mean is ideal for symmetric data without outliers, such as average test scores in education. The median suits skewed data, like income distributions in economics, providing clearer insights into typical values and aiding decision-making in fields like research and policy.

Frequently Asked Questions

What is the difference between mean and median?

When should you use the median over the mean?

How do you handle missing values when calculating mean or median?

Is the mean always greater than the median in skewed data?