Final answer:
Cumulative frequency distribution is calculated by summing the frequencies of all preceding classes with the current class frequency. Relative frequency is the ratio of the class frequency to the total data points. Cumulative relative frequency is found by adding the current row’s relative frequency to the total of the previous relative frequencies.
Step-by-step explanation:
Cumulative Frequency Distribution
To find the cumulative frequency distribution, we start by adding each class frequency to the total of the frequencies of all preceding classes. Here’s how the cumulative frequency distribution would look like for the given classes:
- 10 up to 20: Frequency is 16, Cumulative Frequency is 16 (since it’s the first interval).
- 20 up to 30: Frequency is 19, Cumulative Frequency is 16 + 19 = 35.
- 30 up to 40: Frequency is 29, Cumulative Frequency is 35 + 29 = 64.
- 40 up to 50: Frequency is 8, Cumulative Frequency is 64 + 8 = 72.
Additionally, to calculate the relative frequency, we would divide the frequency by the total number of data points. For instance, if we had a total of 100 data points and a class frequency of 16, the relative frequency would be 16/100 = 0.16. Cumulative relative frequency is then found by adding the relative frequency of the current row to the cumulative relative frequency of the previous row.
A frequency indicates how often a data point occurs. To provide an example with given data, if we had three students who studied for two hours and five students who studied for three hours, the frequencies would be 3 and 5, respectively. In a frequency distribution table, these values would be listed along with their frequencies.
To understand relative frequency in practice, consider a hypothetical class of 35 students. If seven students scored between 70 and 79, the relative frequency for this score range would be 7/35 = 0.20 or 20%.