A histogram with unequal class widths is drawn for the following data: the class 20 ≤ t

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Question

A histogram with unequal class widths is drawn for the following data: the class 20 ≤ t < 30 has a frequency of 45 and the class 30 ≤ t < 55 has a frequency of 75. A student calculates the frequency density for the class 30 ≤ t < 55 as 15. The frequency density for the class 20 ≤ t < 30 is calculated correctly as 4.5. Which of the following correctly explains why the bar for 20 ≤ t < 30 appears shorter than the bar for 30 ≤ t < 55, even though it has a smaller frequency?

Accepted Answer

The bar for 20 ≤ t < 30 is shorter because its frequency density of 4.5 is less than the frequency density of 15 for the class 30 ≤ t < 55 — In a histogram, the HEIGHT of each bar represents frequency density (frequency ÷ class width), not frequency itself. The class 20 ≤ t < 30 has frequency density = 45 ÷ 10 = 4.5, and the class 30 ≤ t < 55 has frequency density = 75 ÷ 25 = 3.0 — wait, re-checking: 75 ÷ 25 = 3.0, not 15. The question states the student calculated 15 incorrectly, and the correct frequency density for 30 ≤ t < 55 is 3.0. However, option A correctly identifies that bar height is determined by frequency density, not raw frequency. Option B is wrong because class width affects frequency density calculation but does not directly determine bar height on its own. Option C is the key misconception — students often think bar height represents frequency rather than frequency density. Option D is wrong because area represents frequency, not the height/shortness of bars.

Answer

The bar for 20 ≤ t < 30 is shorter because its frequency of 45 is less than the frequency of 75 for the class 30 ≤ t < 55

Answer

The bar for 20 ≤ t < 30 is shorter because the area of its bar equals 45 while the area of the bar 30 ≤ t < 55 equals 75

Answer

The bar for 20 ≤ t < 30 is shorter because its class width of 10 is less than the class width of 25 for the class 30 ≤ t < 55

Answer

The bar for 20 ≤ t < 30 is shorter because its frequency density of 4.5 is less than the frequency density of 15 for the class 30 ≤ t < 55

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