Ms. Alison drew a box-and-whisker plot to represent her students’ scores on a midterm test. Josh received 83 on the test. Describe how his score compares with those of his classmates.
a. About 23% scored higher; about 77% scored lower.
b. About 50% scored higher; about 50% scored lower.
c. About 75% scored higher; about 25% scored lower.
d. About 25% scored higher; about 75% scored lower.
To determine how Josh's score compares with those of his classmates using a box-and-whisker plot, you need to identify the quartiles on the plot.
A box-and-whisker plot is divided into several sections:
1. The median (Q2) represents the middle value of the dataset. This is the line dividing the box.
2. The lower quartile (Q1) represents the value below which 25% of the data falls. This is the bottom boundary of the box.
3. The upper quartile (Q3) represents the value below which 75% of the data falls. This is the top boundary of the box.
4. The whiskers, represented by lines extending from the box, show the range of the data excluding any outliers.
To determine how Josh's score compares, you need to look at the quartiles. If Josh's score is at or below Q1, then he scored lower than approximately 25% of his classmates. If his score is above Q3, then he scored higher than approximately 75% of his classmates.
Since it is not specified if Josh's score falls within or outside the quartiles, we cannot provide an exact percentage. However, based on the options provided, the closest answer would be (d) "About 25% scored higher; about 75% scored lower." This assumes that Josh's score is either above Q3 (75%) or between Q1 (25%) and Q3 (75%), but not above Q3.