One week, Freddie the fisherman catches 150 fish. Part a) Complete the table below.
There is also a part b that we will look at later. We’re told that Freddie catches a total of 150 fish. Therefore, the number of cod, mackerel, and bream must add up to 150. The sum of the three frequencies equals 150. We’re also told that the relative frequency of catching a mackerel is 0.62, and the relative frequency of catching bream is 0.24.
In the same way as the sum of probabilities equal one, the sum of the relative frequencies must equal one. If we let the missing number in a relative frequency row for cod be letter 𝑐, then 𝑐 plus 0.62 plus 0.24 must equal one. 0.62 plus 0.24 is equal to 0.86, as 62 plus 24 equals 86. This means that 𝑐 plus 0.86 equals one. Subtracting 0.86 from the left-hand side of the equation gives us 𝑐, as 0.86 minus 0.86 is zero. One minus 0.86 is equal to 0.14. Therefore, 𝑐 is equal to 0.14. The relative frequency with which Freddie the fisherman caught cod is 0.14. It is worth checking on the calculator that 0.14 plus 0.62 plus 0.24 do indeed equal one.
Relative frequency can be calculated by dividing the frequency by the total of the frequencies. The relative frequency of bream, 0.24, has been calculated by dividing 36 by 150. There were 36 bream caught, and there were 150 fish caught altogether. The formula can be rearranged so we can calculate the frequencies. We need to multiply the relative frequency by the total frequencies.
In this question, the total of the frequencies is 150. We can therefore calculate the frequency or the number of cod that were caught by multiplying 0.14 by 150. This is equal to 21. Therefore, Freddie the fisherman caught 21 cod.
We can repeat this process for mackerel. This time, we multiply 0.62 by 150. This is equal to 93. Therefore, Freddie caught 93 mackerel. Once again, it is worth checking by adding 21, 93, and 36 and ensuring that they add up to 150. The missing numbers in the table in the top row are 21 and 93 and in the bottom row 0.14.
The second part of the question says the following. b) The next week, Freddie the fisherman catches 350 fish in total. Assuming the distribution of fish is the same, how many mackerel would you expect Freddie to catch?
The total number of fish caught in this week is 350, and the relative frequency of catching mackerel is 0.62. We can therefore calculate the number of mackerel caught by multiplying 0.62 by 350. This is the same as working out 62 percent of 350. Typing 0.62 multiplied by 350 into the calculator gives us an answer of 217. If the relative frequency remains the same and Freddie catches 350 fish, we would expect 217 of them to be mackerel.