Question

skiing is a snow sport where skiers glide over snowy hills.
the data below represents the number of practices each member of jimenais 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: \(25\)
• Maximum: \(38\)
• Median (\(Q_2\)): Since there are \(n = 10\) data points, the median is the average of the \(5^{th}\) and \(6^{th}\) values. \(\frac{30 + 34}{2}=32\)
• Lower half of data: \(25,28,29,29,30\). Lower quartile (\(Q_1\)): The \(3^{rd}\) value of the lower - half. \(Q_1 = 29\)
• Upper half of data: \(34,35,35,37,38\). Upper quartile (\(Q_3\)): The \(3^{rd}\) value of the upper - half. \(Q_3=35\)

Step2: Analyze each box - plot

• For a box - plot, the left - most whisker is the minimum, the right - most whisker is the maximum, the left - side of the box is \(Q_1\), the middle line of the box is \(Q_2\), and the right - side of the box is \(Q_3\).
• Option A: The left - side of the box (lower quartile) should be \(29\), the middle line (median) should be \(32\), and the right - side of the box (upper quartile) should be \(35\). This option does not match.
• Option B: The left - side of the box (lower quartile) should be \(29\), the middle line (median) should be \(32\), and the right - side of the box (upper quartile) should be \(35\). This option does not match.
• Option C: The minimum is \(25\), the maximum is \(38\), \(Q_1 = 29\), \(Q_2=32\), \(Q_3 = 35\). This option matches the calculated values.

Answer:

C.