the number of vehicle passing through an intersection during each 15-minute period was recorded. the results are shown below. construct a frequency distribution (and a relative frequency distribution) for the vehicles passing through the intersection in a 15-minute period. use 5 classes beginning with a lower class limit of 10 vehicles and use a class width of 5 vehicles. 23 25 23 26 26 23 28 25 33 29 29 27 22 29 23 18 13 25 25 25 14 22 17 28 15 17 28 22 18 31 11 27

To construct a frequency distribution, we need to:

Step 1: Determine the range of vehicles passing through the intersection. The range is the difference between the highest and lowest values in the data set.

Range = Highest value - Lowest value
Range = 33 - 11
Range = 22

Step 2: Determine the class width. The class width is the interval size for each class.

Class width = Range / Number of classes
Class width = 22 / 5
Class width ≈ 4.4

However, we need to use a class width of 5 vehicles, so we round up to the nearest whole number. Therefore, our class width is 5.

Step 3: Determine the lower class limit for the first class. In this case, the lower class limit is given as 10 vehicles.

Lower class limit for the first class = 10

Step 4: Calculate the upper class limit for each class by adding the class width to the lower class limit.

Class 1: 10 - 14
Class 2: 15 - 19
Class 3: 20 - 24
Class 4: 25 - 29
Class 5: 30 - 34

Step 5: Count the frequency of vehicles in each class by tallying the number of data points that fall within each class.

Class 1: 3 (13, 14)
Class 2: 7 (15, 17, 18, 18, 22, 22, 23)
Class 3: 7 (23, 23, 25, 25, 25, 26, 27)
Class 4: 8 (25, 26, 27, 28, 28, 29, 29, 29)
Class 5: 2 (31, 33)

Now we can construct the frequency distribution table:

Class | Frequency
-------------------
10-14 | 3
15-19 | 7
20-24 | 7
25-29 | 8
30-34 | 2

To construct the relative frequency distribution, we need to divide the frequency of each class by the total number of vehicles:

Total number of vehicles = Sum of all frequencies = 3 + 7 + 7 + 8 + 2 = 27

Relative frequency = Frequency / Total number of vehicles

Class | Frequency | Relative Frequency
----------------------------------------
10-14 | 3 | 3/27 ≈ 0.111
15-19 | 7 | 7/27 ≈ 0.259
20-24 | 7 | 7/27 ≈ 0.259
25-29 | 8 | 8/27 ≈ 0.296
30-34 | 2 | 2/27 ≈ 0.074

This is the frequency distribution and relative frequency distribution of the vehicles passing through the intersection in a 15-minute period using the given data.