Question

the data below show the donations, in dollars, a charity received from 8 of its donors at a fund - raising event.
440, 580, 480, 600, 720, 720, 800, 840
which box plot correctly represents these data?
a
donations (in dollars)
400 500 600 700 800 900
b
donations (in dollars)
400 500 600 700 800 900
c
donations (in dollars)
400 500 600 700 800 900
d
donations (in dollars)
400 500 600 700 800 900

Explanation:

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

The data set is \(440,510,600,600,720,720,800,840\).

• Minimum: \(440\)
• Maximum: \(840\)
• Median (\(Q_2\)): Since \(n = 8\) (even), \(\frac{600 + 720}{2}=660\)
• Lower half: \(440,510,600,600\), \(Q_1=\frac{510 + 600}{2}=555\)
• Upper half: \(720,720,800,840\), \(Q_3=\frac{720+800}{2} = 760\)

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 minimum is not \(440\) (the left - most point is not at the correct position for \(440\) relative to the scale).
• For option B:
• Minimum \(=440\), maximum \(=840\)
• \(Q_1 = 555\) (left - edge of the box), \(Q_2=660\) (middle line of the box), \(Q_3 = 760\) (right - edge of the box)
• For option C: The left - most point (minimum) is not \(440\) (incorrect position relative to the scale).
• For option D: The middle line of the box (median) is not \(660\) (incorrect position relative to the scale).

Answer:

B.