Question

1. the box - and - whisker plot below represents a set of grades in a college statistics class.which interval contains exactly 50% of the grades?1) 63 - 88 3) 75 - 812) 63 - 95 4) 75 - 88

Explanation:

Step1: Recall Box - Whisker Plot Properties

In a box - and - whisker plot, the box represents the middle 50% of the data (the inter - quartile range, IQR). The box is between the first quartile (\(Q_1\)) and the third quartile (\(Q_3\)), and the data within the box (between \(Q_1\) and \(Q_3\)) contains 50% of the data.

Step2: Analyze the Plot and Intervals

Looking at the number line, the box seems to span from around 75 to 88 (by looking at the markings: 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96). Let's check each interval:

• Option 1: 63 - 88. The lower bound 63 is outside the box's lower range (the box starts higher), so this interval includes more than 50% (includes data below the box).
• Option 2: 63 - 95. This includes almost all the data (from low to high), so it's more than 50%.
• Option 3: 75 - 81. This is a subset of the box's range, so it includes less than 50%.
• Option 4: 75 - 88. This corresponds to the range of the box in the box - and - whisker plot, which contains the middle 50% of the data.

Answer:

1. 75 - 88