Question

1 the box plot represents the distribution of speeds, in miles per hour, of 100 cars as they passed through a busy intersection. 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 whisker end represents the smallest value. From the box - plot, the smallest value is 8. This means that the slowest - moving car among the 100 cars passed through the intersection at a speed of 8 miles per hour.

Step2: Identify largest value from box - plot

The right - most whisker end represents the largest value. From the box - plot, the largest value is 44. This means that the fastest - moving car among the 100 cars passed through the intersection at a speed of 44 miles per hour.

Step3: Identify median from box - plot

The line inside the box represents the median. From the box - plot, the median is 20. This means that half of the 100 cars (50 cars) had speeds less than or equal to 20 miles per hour and the other half had speeds greater than or equal to 20 miles per hour as they passed through the intersection.

Step4: Identify first quartile from box - plot

The left - hand side of the box represents the first quartile (Q1). From the box - plot, Q1 is 12. This means that 25% of the 100 cars (25 cars) had speeds less than or equal to 12 miles per hour as they passed through the intersection.

Step5: Identify third quartile from box - plot

The right - hand side of the box represents the third quartile (Q3). From the box - plot, Q3 is 24. This means that 75% of the 100 cars (75 cars) had speeds less than or equal to 24 miles per hour as they passed through the intersection.

Answer:

a. 8; The slowest - moving car among the 100 cars passed through the intersection at 8 miles per hour.
b. 44; The fastest - moving car among the 100 cars passed through the intersection at 44 miles per hour.
c. 20; Half of the 100 cars had speeds less than or equal to 20 miles per hour and the other half had speeds greater than or equal to 20 miles per hour as they passed through the intersection.
d. 12; 25% of the 100 cars had speeds less than or equal to 12 miles per hour as they passed through the intersection.
e. 24; 75% of the 100 cars had speeds less than or equal to 24 miles per hour as they passed through the intersection.