Question

question 14 (multiple choice worth 2 points) (box plots mc) the box plot represents the scores on quizzes in a history class. history quizzes scores on quizzes (x - axis from 69 to 87) what value does 75% of the data lie above? find the value. options: the lower quartile (q1), and it is 75; the lower quartile (q1), and it is 79; the upper quartile (q3), and it is 82; the upper quartile (q3), and it is 84

Explanation:

Step1: Recall Quartile Definition

The lower quartile (Q1) is the value where 25% of data is below it (75% above). The upper quartile (Q3) has 75% below, 25% above. We need 75% above, so focus on Q1.

Step2: Analyze Box Plot for Q1

In a box plot, the left edge of the box is Q1. From the plot, the left box edge aligns with 75? Wait, no—wait, the x - axis: the box starts at 75? Wait, no, re - check. Wait, the options: first option says Q1 is 75. Wait, let's think again. The lower quartile (Q1) is the 25th percentile, meaning 75% of data is above Q1. So we need to find Q1. Looking at the box plot, the left side of the box (Q1) is at 75? Wait, no, the first option: "The lower quartile (Q1), and it is 75". Wait, let's check the options. Wait, the first option: Q1 is 75, which would mean 75% of data is above 75. Let's verify the quartile concept: Q1 divides the data into lower 25% and upper 75%. So the value where 75% of data lies above is Q1. Now, looking at the box plot, the left end of the box (Q1) is at 75? Wait, the x - axis labels: 69,70,71,72,73,74,75,76,... The box starts at 75? Wait, the first option is "The lower quartile (Q1), and it is 75". Let's check the other options. The second option says Q1 is 79, which doesn't match. The third and fourth are Q3 (which has 25% above), so they are wrong. So the correct one is the first option? Wait, no, wait the box plot: maybe I misread. Wait, the box plot's left whisker goes to 69, then the box starts at 75? Wait, the first option: "The lower quartile (Q1), and it is 75". So Q1 is 75, so 75% of data is above 75. So the correct option is the first one? Wait, no, wait the options:

Option 1: The lower quartile (Q1), and it is 75

Option 2: The lower quartile (Q1), and it is 79

Option 3: The upper quartile (Q3), and it is 82

Option 4: The upper quartile (Q3), and it is 84

Since Q1 is the 25th percentile (75% above), we need Q1. Now, looking at the box plot, the left side of the box (Q1) is at 75. So the correct option is the first one? Wait, no, maybe I made a mistake. Wait, the box plot: the left edge of the box is Q1. Let's see the x - axis: the box is from, say, 75 to 82? Wait, no, the first box is from 75 to 79, then the second from 79 to 82? Wait, maybe the left box (first quartile to median) is 75 - 79, and median to Q3 is 79 - 82. Wait, no, the box has two parts? Wait, the box plot has a box divided into two parts, maybe the median is at 79. So Q1 is 75? Wait, the first option says Q1 is 75. So the answer should be the first option? Wait, no, wait the question is "What value does 75% of the data lie above?". So 75% above means 25% below, which is Q1. So we need to find Q1. From the box plot, the left end of the box (Q1) is at 75. So the correct option is:

Answer:

A. The lower quartile (Q1), and it is 75