Creating a Box Plot

Pre-Algebra · Axiom Academy

Find the five-number summary of a data set, then draw its box plot — one step at a time. A teacher records the scores of 15 students on a short quiz: Find the five-number summary (minimum, Q_1 , median, Q_3 , maximum) and use it to draw a box plot of the scores. Nice work — you turned a raw list of 15 scores into a five-number summary and a finished box plot. Order first: every box-plot statistic depends on the data being sorted from least to greatest. The five-number summary: minimum, Q_1 , median, Q_3 , and maximum together describe the whole distribution. Odd-sized data: with 15 values the median is the single middle (8th) value; with an even count it would be the average of the two middle values. Quartiles: Q_1 is the median of the lower half and Q_3 the median of the upper half — here, the median itself is excluded from both halves. Reading the plot: the box covers the middle of the data ( Q_1 to Q_3 ), the line inside is the median, and the whiskers stretch out to the minimum and maximum. Spread: the interquartile range measures how spread out the middle half of the scores is. Box plots let you compare data sets and spot outliers at a glance — a quick visual summary of where the data sits and how far it spreads.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.