Question

skiing is a snow sport where skiers glide over snowy hills.
the data below represents the number of practices each member of jimenas ski team attended.
25, 28, 29, 29, 30, 34, 35, 35, 37, 38
which box plot correctly summarizes the data?
choose 1 answer:
a
b
c

Explanation:

Step1: Find the minimum, maximum, median, lower quartile, and upper quartile

• The data set is \(25, 28, 29, 29, 30, 34, 35, 35, 37, 38\)
• Minimum value: \(25\)
• Maximum value: \(38\)
• Median (\(Q_2\)): Since \(n = 10\) (even), \(Q_2=\frac{30 + 34}{2}=32\)
• Lower half of data: \(25, 28, 29, 29, 30\). Lower quartile (\(Q_1\)): \(29\)
• Upper half of data: \(34, 35, 35, 37, 38\). Upper quartile (\(Q_3\)): \(35\)

Step2: Analyze each box - plot

• In a box - plot, the left - most point is the minimum, the right - most point is the maximum, the left - edge of the box is \(Q_1\), the middle line of the box is \(Q_2\), and the right - edge of the box is \(Q_3\)
• For option A: The middle line (median) should be at \(32\), but in option A, the box is skewed to the right in a wrong proportion.
• For option B: The left - edge of the box (\(Q_1 = 29\)), middle line (\(Q_2=32\)), right - edge of the box (\(Q_3 = 35\)), minimum (\(25\)), and maximum (\(38\)) match our calculated values.
• For option C: The box is divided into two equal parts (which would imply \(Q_1=Q_2 - k\) and \(Q_3=Q_2 + k\) for some \(k\), but our \(Q_1 = 29\), \(Q_2=32\), \(Q_3 = 35\) do not satisfy this equal - division condition)

Answer:

B.