Answer :
Sure, let's go through the process step-by-step to construct a cumulative frequency distribution.
1. Understanding the data: We have a frequency distribution showing time (in hours) workers spend each year looking for a parking space. The class boundaries and their frequencies are given.
2. Determine each cumulative frequency: We'll calculate the cumulative frequency for each class, which is the sum of the frequencies for that class plus all previous classes.
3. Calculate cumulative frequencies:
- Less than 26.5: Start with a cumulative frequency of 0 because no data falls below this class boundary.
- Less than 31.5: Add the frequency of the first class (24) to the previous cumulative frequency (0), giving us 24.
- Less than 36.5: Add the frequency of the second class (25) to the cumulative frequency of the previous class (24), resulting in 49.
- Less than 41.5: Add the frequency of the third class (19) to the cumulative frequency of the previous class (49), totaling 68.
- Less than 46.5: Add the frequency of the fourth class (15) to the cumulative frequency of the previous class (68), resulting in 83.
- Less than 51.5: Add the frequency of the fifth class (10) to the cumulative frequency from the previous class (83), giving 93.
- Less than 56.5: Add the frequency of the sixth class (3) to the cumulative frequency from the previous class (93), totaling 96.
4. Cumulative frequency distribution:
- Less than 26.5: 0
- Less than 31.5: 24
- Less than 36.5: 49
- Less than 41.5: 68
- Less than 46.5: 83
- Less than 51.5: 93
- Less than 56.5: 96
This cumulative frequency distribution shows us how the frequencies accumulate as we move up through the class boundaries, providing a comprehensive overview of the data.
1. Understanding the data: We have a frequency distribution showing time (in hours) workers spend each year looking for a parking space. The class boundaries and their frequencies are given.
2. Determine each cumulative frequency: We'll calculate the cumulative frequency for each class, which is the sum of the frequencies for that class plus all previous classes.
3. Calculate cumulative frequencies:
- Less than 26.5: Start with a cumulative frequency of 0 because no data falls below this class boundary.
- Less than 31.5: Add the frequency of the first class (24) to the previous cumulative frequency (0), giving us 24.
- Less than 36.5: Add the frequency of the second class (25) to the cumulative frequency of the previous class (24), resulting in 49.
- Less than 41.5: Add the frequency of the third class (19) to the cumulative frequency of the previous class (49), totaling 68.
- Less than 46.5: Add the frequency of the fourth class (15) to the cumulative frequency of the previous class (68), resulting in 83.
- Less than 51.5: Add the frequency of the fifth class (10) to the cumulative frequency from the previous class (83), giving 93.
- Less than 56.5: Add the frequency of the sixth class (3) to the cumulative frequency from the previous class (93), totaling 96.
4. Cumulative frequency distribution:
- Less than 26.5: 0
- Less than 31.5: 24
- Less than 36.5: 49
- Less than 41.5: 68
- Less than 46.5: 83
- Less than 51.5: 93
- Less than 56.5: 96
This cumulative frequency distribution shows us how the frequencies accumulate as we move up through the class boundaries, providing a comprehensive overview of the data.