Question

1. the box plot represents the distribution of speeds, in miles per hour, of 100 cars as they passed through a busy intersection. speed of cars (miles per hour) a. what is the smallest value in the data set? interpret this value in the situation. b. what is the largest value in the data set? interpret this value in the situation. c. what is the median? interpret this value in the situation. d. what is the first quartile (q1)? interpret this value in the situation. e. what is the third quartile (q3)? interpret this value in the situation.

Explanation:

Step1: Identify smallest value from box - plot

The left - most end of the whisker represents the smallest value. In the given box - plot, the smallest value is 4 miles per hour. This means that the slowest car among the 100 cars that passed through the intersection was moving at 4 miles per hour.

Step2: Identify largest value from box - plot

The right - most end of the whisker represents the largest value. In the given box - plot, the largest value is 48 miles per hour. This means that the fastest car among the 100 cars that passed through the intersection was moving at 48 miles per hour.

Step3: Identify median from box - plot

The line inside the box represents the median. In the given box - plot, the median is 20 miles per hour. This means that half of the 100 cars (i.e., 50 cars) were moving at speeds less than or equal to 20 miles per hour and the other half were moving at speeds greater than or equal to 20 miles per hour.

Step4: Identify first quartile from box - plot

The left - hand side of the box represents the first quartile (Q1). In the given box - plot, Q1 is 12 miles per hour. This means that 25% of the 100 cars (i.e., 25 cars) were moving at speeds less than or equal to 12 miles per hour.

Step5: Identify third quartile from box - plot

The right - hand side of the box represents the third quartile (Q3). In the given box - plot, Q3 is 24 miles per hour. This means that 75% of the 100 cars (i.e., 75 cars) were moving at speeds less than or equal to 24 miles per hour.

Answer:

a. The smallest value is 4 miles per hour. It is the speed of the slowest car among the 100 cars.
b. The largest value is 48 miles per hour. It is the speed of the fastest car among the 100 cars.
c. The median is 20 miles per hour. Half of the cars had speeds less than or equal to this value.
d. The first quartile (Q1) is 12 miles per hour. 25% of the cars had speeds less than or equal to this value.
e. The third quartile (Q3) is 24 miles per hour. 75% of the cars had speeds less than or equal to this value.