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# How to Estimate the Mean and Median of Any Histogram

AÂ histogramÂ 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, itâ€™s not always obvious what the mean and median values are just from looking at the histograms.

And while itâ€™s not possible to find the exact mean and median values of a distribution just from looking at a histogram, itâ€™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: Î£mini / N

where:

• mi: The midpoint of the ith bin
• ni: The frequency of the ith 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 â€“ 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 â€“ 9) / 10) * 9 =Â 24.15.

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