Interpret box-and-whisker plots

Learning Objectives Identify the five-number summary (minimum, first quartile, median, third quartile, maximum) from a box-and-whisker plot. Explain what each section of a box-and-whisker plot represents in terms of data distribution. Calculate the range and interquartile range (IQR) of a data set using a box-and-whisker plot. Describe the spread and center of a data set based on its box-and-whisker plot. Compare two or more data sets by interpreting their respective box-and-whisker plots. Relate percentages to the different sections of a box-and-whisker plot. Have you ever wondered how to quickly compare test scores from two different classes, or see how spread out the ages are in a group? 📊 Box-and-whisker plots are like data superheroes that help us do just that! In thi...

TermDefinitionExample Box-and-Whisker PlotA type of graph that displays the five-number summary of a set of data: minimum, first quartile, median, third quartile, and maximum. It shows the spread and center of the data.A box-and-whisker plot showing student test scores might have a box from 70 to 90, with a line at 80, and whiskers extending to 50 and 100. Median (Q2)The middle value of a data set when the numbers are arranged in order from least to greatest. It divides the data into two equal halves.In the data set {2, 5, 7, 10, 12}, the median is 7. On a box plot, it's the line inside the box. First Quartile (Q1)The median of the lower half of a data set. It marks the point below which 25% of the data falls.If the lower half of a data set is {2, 5, 7}, the first quartile (Q1) would...

Five-Number Summary Identification The box-and-whisker plot visually represents the Minimum Value, First Quartile (Q1), Median (Q2), Third Quartile (Q3), and Maximum Value. To find these values, simply read the numbers on the number line corresponding to the ends of the whiskers, the edges of the box, and the line inside the box. Range Calculation $\text{Range} = \text{Maximum Value} - \text{Minimum Value}$ The range tells you the total spread of the entire data set, from the smallest to the largest value. Interquartile Range (IQR) Calculation $\text{IQR} = Q_3 - Q_1$ The IQR tells you the spread of the middle 50% of the data, which is often a more stable measure of spread than the full range because it ignores extreme values. Percentage Distribution Rule Each...