The relative frequency of direct hits of category 1 is 0.3993. Notice that the cumulative relative frequency of category 1 and 2 hits, the sum of the relative frequency of both categories, is 0.6630. The relative frequency of category 2 hits is 0.2637. Consequently, the relative frequency of direct hits of category 1 is 0.6630 - 0.2637 = 0.3993.
The relative frequency of direct hits of category 4 or more is 0.0769. Observe that the cumulative relative of the value “3" is 0.6630 + 0.2601 = 0.9231. This follows from the fact that the cumulative relative frequency of the value “2" is 0.6630 and the relative frequency of the value “3" is 0.2601. The total cumulative relative frequency is 1.0000. The relative frequency of direct hits of category 4 or more is the difference between the total cumulative relative frequency and cumulative relative frequency of 3 hits: 1.0000 - 0.9231 = 0.0769.
The total number of cows that were involved in this study is 45. The object “freq" contain the table of frequency of the cows, divided according to the number of calves that they had. The cumulative frequency of all the cows that had 7 calves or less, which includes all cows in the study, is reported under the number “7" in the output of the expression “cumsum(freq)". This number is 45.
The number of cows that gave birth to a total of 4 calves is 10. Indeed, the cumulative frequency of cows that gave birth to 4 calves or less is 28. The cumulative frequency of cows that gave birth to 3 calves or less is 18. The frequency of cows that gave birth to exactly 4 calves is the difference between these two numbers: 28 - 18 = 10.
The relative frequency of cows that gave birth to at least 4 calves is \(27/45 = 0.6\text{.}\) Notice that the cumulative frequency of cows that gave at most 3 calves is 18. The total number of cows is 45. Hence, the number of cows with 4 or more calves is the difference between these two numbers: 45 - 18 = 27. The relative frequency of such cows is the ratio between this number and the total number of cows: \(27/45 = 0.6\text{.}\)
