Back to Represent data with plots — Problem 4 · Task Set 1

Exercises: Represent Data with Plots on the Real Number Line

Work through each section in order. For plots, read carefully: dot plots show every individual value, histograms group values into intervals (bars touch), and box plots summarize data with the five-number summary (minimum, Q1, median, Q3, maximum). Write explanation answers in complete sentences.

Grade 9·22 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-id-a-1

Work through problems with immediate feedback

Fluency Practice

Read each plot and answer. Use the displayed values.

$Box plot of ages; the median line at 24 is left of the center of the box from 17 to 32.$

Look again at the box plot of ages (min 12, Q1 17, median 24, Q3 32, max 50). A student says the box plot must be drawn wrong because the median line is not in the center of the box. Which response is correct?

The plot is correct. The median line need not be centered; it sits closer to Q1 here because the lower half of the box (17 to 24) is more compressed than the upper half (24 to 32), indicating right skew.

The student is right; the median line must always split the box into two equal halves.

The plot is wrong because the median should equal the midpoint of Q1 and Q3.

The median line should be at the center of the whole number line.