Measures of Central Tendency for Ungrouped Data
Enter raw numerical data. This tool computes the mean, median, and mode and draws a histogram with the mean, median, and mode marked on the axis.
Measures of Central Tendency for Ungrouped Data
Statistics • Numerical Descriptive Measures
Frequently Asked Questions
How is the mean calculated for ungrouped data?
The mean is the sum of all observations divided by the number of observations. In symbols, mean = (x1 + x2 + ... + xn) / n.
How do you find the median when there are an even number of values?
First sort the data from smallest to largest. If n is even, the median is the average of the two middle values in the ordered list.
What if there is more than one mode or no mode?
If multiple values share the highest frequency, the dataset is multimodal and all of those values are modes. If all values occur with the same frequency, then there is no mode.
Why can the mean, median, and mode be different?
They summarize center in different ways: the mean uses all values, the median depends on order, and the mode depends on frequency. Outliers can pull the mean toward extreme values while the median is more resistant.
How does the histogram help interpret mean, median, and mode?
The histogram shows the overall shape of the distribution, and marking mean, median, and mode helps indicate symmetry or skewness. For example, in a right-skewed distribution the mean is often to the right of the median and mode.