Question

lesson 3 practice problems
1 the box - plot represents the distribution of speeds, in miles per hour, of cars passed through a busy intersection.
the box - plot shows values such as 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 (speeds of cars in 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.

Step2: Identify largest value from box - plot

The right - most end of the whisker represents the largest value.

Step3: Identify median from box - plot

The line inside the box represents the median. It divides the data set into two equal halves. In the context of car speeds, half of the cars had speeds less than this value and half had speeds greater.

Step4: Identify first quartile from box - plot

The left - hand side of the box represents the first quartile (Q1). 25% of the data values are less than or equal to this value. In terms of car speeds, 25% of the cars had speeds less than or equal to this value.

Step5: Identify third quartile from box - plot

The right - hand side of the box represents the third quartile (Q3). 75% of the data values are less than or equal to this value. In terms of car speeds, 75% of the cars had speeds less than or equal to this value.

However, since the box - plot is not fully visible in the provided image, we can't give numerical answers. But the general interpretations are as above.

If we assume a typical box - plot structure and values from the visible scale:
a. The smallest value is 4 (assuming the left - most value on the scale). It means the slowest car speed recorded at the busy intersection was 4 miles per hour.
b. The largest value is 48 (assuming the right - most value on the scale). It means the fastest car speed recorded at the busy intersection was 48 miles per hour.
c. If we assume the middle of the box is at 24, the median is 24. This implies that half of the cars had speeds less than 24 miles per hour and half had speeds greater than 24 miles per hour at the busy intersection.
d. If the left - hand side of the box is at 16, Q1 is 16. This means that 25% of the cars had speeds of 16 miles per hour or less at the busy intersection.
e. If the right - hand side of the box is at 36, Q3 is 36. This means that 75% of the cars had speeds of 36 miles per hour or less at the busy intersection.

Answer:

a. 4 miles per hour. It is the slowest car speed recorded.
b. 48 miles per hour. It is the fastest car speed recorded.
c. 24 miles per hour. Half of the cars had speeds less than this.
d. 16 miles per hour. 25% of the cars had speeds of this value or less.
e. 36 miles per hour. 75% of the cars had speeds of this value or less.