Mrs. Little creates a boxplot for the test scores on her latest math test. She finds that the interquartile range is 20 points. What does this mean?
Between 25% and 75% of the scores is 20 points.
The interquartile range (IQR) is a statistical measure that represents the spread or dispersion of the middle 50% of the data in a distribution. In this case, Mrs. Little calculated the IQR for the test scores on her latest math test and found it to be 20 points.
To understand the IQR, you first need to understand quartiles. Quartiles divide a dataset into four equal parts. The first quartile (Q1) represents the 25th percentile, which is the data point below which 25% of the data falls. The third quartile (Q3) represents the 75th percentile, which is the data point below which 75% of the data falls. Hence, the IQR is the difference between Q3 and Q1.
In Mrs. Little's case, the IQR of 20 points suggests that the middle 50% of test scores fall between Q1 and Q3, with a spread of 20 points. This range provides information about the variability or dispersion of the scores within this middle section.