Answer: Class 1 (4-8): 6
Class 2 (9-13): 4
Class 3 (14-18): 2
Class 4 (19-23): 8
Explanation:
To construct a frequency table for the given data, we need to group the hours spent commuting into four classes. The given data is as follows: 4, 5, 17, 22, 13, 19, 22, 4, 20, 21, 7, 12, 23, 13, 13, 8, 22, 7, 20, 23.
Step 1: Sort the data in ascending order: 4, 4, 5, 7, 7, 8, 12, 13, 13, 13, 17, 19, 20, 20, 21, 22, 22, 22, 23, 23.
Step 2: Determine the range of the data by subtracting the smallest value from the largest value: 23 - 4 = 19.
Step 3: Calculate the width of each class by dividing the range by the desired number of classes. In this case, we want four classes, so 19 / 4 = 4.75. Since it's not practical to have a fractional width, we round up to 5.
Step 4: Determine the lower class limits for each class. Start with the smallest value, which is 4, and add the class width to obtain the next lower limit: 4, 9, 14, 19.
Step 5: Use the lower class limits to determine the upper class limits. Subtract 1 from the next lower limit to get the upper limit: 8, 13, 18, 23.
Step 6: Count how many values fall within each class interval and record the frequencies: Class 1 (4-8): 4, 5, 4, 7, 7, 8 (frequency = 6). Class 2 (9-13): 12, 13, 13, 13 (frequency = 4). Class 3 (14-18): 17, 19 (frequency = 2). Class 4 (19-23): 20, 20, 21, 22, 22, 22, 23, 23 (frequency = 8).
Step 7: Create the frequency table by listing the class intervals and their respective frequencies: Class 1 (4-8): 6. Class 2 (9-13): 4. Class 3 (14-18): 2. Class 4 (19-23): 8.
So, the frequency table for the given data using four classes is as follows:
Class 1 (4-8): 6
Class 2 (9-13): 4
Class 3 (14-18): 2
Class 4 (19-23): 8
This table shows the number of employees who spend a certain number of hours commuting to and from work each week within each class interval.