Question

lesson 3
practice problems
6 problems
1 the box plot represents the distribution of speeds, in miles per hour, of 100 cars as they passed through a busy intersection.
4 8 12 16 20 24 28 32 36 40 44 48
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 point of the whisker represents the smallest value. From the box - plot, the smallest value is 4. This means that the slowest speed of the 100 cars that passed through the busy intersection was 4 miles per hour.

Step2: Identify largest value from box - plot

The right - most point of the whisker represents the largest value. The largest value is 48. This means that the fastest speed of the 100 cars that passed through the busy intersection was 48 miles per hour.

Step3: Find the median

The line inside the box represents the median. 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.

Step4: Find the first quartile (Q1)

The left - hand side of the box represents Q1. Q1 is 12. This means that 25% of the 100 cars (25 cars) had speeds less than or equal to 12 miles per hour.

Step5: Find the third quartile (Q3)

The right - hand side of the box represents Q3. Q3 is 32. This means that 75% of the 100 cars (75 cars) had speeds less than or equal to 32 miles per hour.

Answer:

a. 4; The slowest speed of the 100 cars was 4 miles per hour.
b. 48; The fastest speed of the 100 cars was 48 miles per hour.
c. 20; Half of the cars had speeds less than or equal to 20 miles per hour.
d. 12; 25% of the cars had speeds less than or equal to 12 miles per hour.
e. 32; 75% of the cars had speeds less than or equal to 32 miles per hour.