To calculate the interquartile range (IQR) from a histogram, you need to identify the first quartile (Q1) and the third quartile (Q3), and then subtract Q1 from Q3.

The interquartile range (IQR) is a measure of the spread of the middle 50% of your data. It is calculated using the formula:

Here, the first quartile (Q1) is the value below which 25% of the data falls, while the third quartile (Q3) is the value below which 75% of the data falls.

To find these quartiles using a histogram, you first need to determine the cumulative frequency. Begin by summing the frequencies of each bar to create a running total. This cumulative frequency will help you pinpoint where 25% and 75% of the data are located. For instance, if you have a total of 100 data points, Q1 corresponds to the 25th data point, and Q3 corresponds to the 75th data point.

Next, locate these data points on the histogram. If the 25th data point falls within a specific bar, you will need to estimate the exact value of Q1 within that bar. Repeat this process for the 75th data point to find Q3. If the data points do not align perfectly with the boundaries of the bars, you may need to use interpolation to estimate the values accurately.

Once you have determined both Q1 and Q3, you can calculate the IQR by subtracting Q1 from Q3. This resulting value indicates the range within which the middle 50% of your data lies, providing insight into the spread and variability of your dataset.