Ms. Alison drew a box-and-whisker plot to represent her students’ scores on a midterm test. Josh received 53 on the test. Describe how his score compares with those of his classmates.
a. About 25% scored higher; about 75% scored lower.
b. About 50% scored higher; about 50% scored lower.
c. About 87% scored higher; about 13% scored lower.
d. About 75% scored higher; about 25% scored lower.
More data needed. Cannot copy and paste here.
To determine how Josh's score compares with his classmates, we need to analyze the box-and-whisker plot. A box-and-whisker plot represents the distribution of a dataset by displaying the minimum, first quartile (25th percentile), median (50th percentile), third quartile (75th percentile), and maximum values.
Since no specific information about the dataset is given, we must make some assumptions. In a symmetrical dataset, the median (50th percentile) divides the data into two equal halves. However, in a skewed dataset, the median may not be the dividing point.
Now, let's examine the options.
a. About 25% scored higher; about 75% scored lower.
This option suggests that Josh's score is higher than only 25% of his classmates. However, this assumes that Josh's score is at the lower end of the dataset. There is no indication or specific information to support this assumption.
b. About 50% scored higher; about 50% scored lower.
This option suggests that Josh's score is higher than 50% of his classmates. Since the median divides the dataset into equal halves, this option is a reasonable estimate if we assume the data is symmetrical. However, we cannot conclusively choose this option without further information about the shape of the distribution.
c. About 87% scored higher; about 13% scored lower.
This option suggests that Josh's score is higher than 87% of his classmates. This estimate assumes that Josh's score is relatively low compared to the rest of the dataset. However, similar to option (a), we cannot make this assumption without additional information.
d. About 75% scored higher; about 25% scored lower.
This option suggests that Josh's score is higher than 75% of his classmates. Assuming the data is symmetrical, this is a reasonable estimate. However, without any specific information about the data, we cannot say for certain.
Given the lack of specific information about the dataset and the assumptions required for any of the options, we cannot definitively determine how Josh's score compares to his classmates based solely on the box-and-whisker plot provided.