A **histogram** is a chart that helps us visualize the distribution of values in a dataset.

The x-axis of a histogram displays bins of data values and the y-axis tells us how many observations in a dataset fall in each bin.

Although histograms are useful for visualizing distributions, it’s not always obvious what the **mean** and **median** values are just from looking at the histograms.

And while it’s not possible to find the exact mean and median values of a distribution just from looking at a histogram, it’s possible to estimate both values. This tutorial explains how to do so.

**How to Estimate the Mean of a Histogram**

We can use the following formula to find the best estimate of the mean of any histogram:

**Best Estimate of Mean:** Σm_{i}n_{i} / N

where:

**m**The midpoint of the i_{i}:^{th}bin**n**The frequency of the i_{i}:^{th}bin**N:**The total sample size

For example, consider the following histogram:

Our best estimate of the mean would be:

Mean = (5.5*2 + 15.5*7 + 25.5*10 + 35.5*3 + 45.5*1) / 23 = **22.89**.

By looking at the histogram, this seems like a reasonable estimate of the mean.

**How to Estimate the Median of a Histogram**

We can use the following formula to find the best estimate of the median of any histogram:

**Best Estimate of Median:** L + ( (n/2 – F) / f ) * w

where:

**L:**The lower limit of the median group**n:**The total number of observations**F:**The cumulative frequency up to the median group**f:**The frequency of the median group**w:**The width of the median group

Once again, consider the following histogram:

Our best estimate of the median would be:

Median = 21 + ( (25/2 – 9) / 10) * 9 = **24.15**.

From looking at the histogram, this also seems to be a reasonable estimate of the median.

**Related:** How to Estimate the Standard Deviation of Any Histogram

**Additional Resources**

How to Find Mean, Median, & Mode in Stem-and-Leaf Plots

How to Calculate Mean from Frequency Tables

When to Use Mean vs. Median

n = 23 not 25, in the last example

This wasn’t helpful, I dont understand the letters this made no sense 🙂