The first value identified in a ratio must be to the left of the colon : and the second value must be to the right of the colon 1st value : 2nd value. For example, in a total of 20 coin tosses where there are 12 heads and 8 tails, the ratio of heads to tails is Alternatively, the ratio of tails to heads is A rate is a measurement of one value for a variable in relation to another measured quantity. For example, in a total of 20 coin tosses where there are 12 heads and 8 tails, the rate is 12 heads per 20 coin tosses.
Alternatively, the rate is 8 tails per 20 coin tosses. A proportion describes the share of one value for a variable in relation to a whole. It is calculated by dividing the number of times a particular value for a variable has been observed, by the total number of values in the population.
Twenty students were asked how many hours they worked per day. Their responses, in hours, are as follows: 5, 6, 3, 3, 2, 4, 7, 5, 2, 3, 5, 6, 5, 4, 4, 3, 5, 2, 5, 3. The following table lists the different data values in ascending order and their frequencies. In this research, 3 students studied for 2 hours. A frequency is the number of times a value of the data occurs.
According to the table, there are three students who work two hours, five students who work three hours, and so on. The sum of the values in the frequency column, 20, represents the total number of students included in the sample.
A relative frequency is the ratio fraction or proportion of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes. To find the relative frequencies, divide each frequency by the total number of students in the sample—in this case, Consequently, the vertical axis would have to be scaled according to the largest frequency. An alternative is to use relative frequencies to describe how many values are in each interval relative to the total number of values.
Multiplying by gives you the percentage, This means that Here is what you get for the rest of the data:. Problem C1 Use only the relative frequencies from the table to answer the questions below. Give your answers as percentages, to the nearest 10th of a percent, or explain why the answer cannot be found from the table. What percentage of the responses are in the 70s and below? What percentage of the responses are 80 or higher? What percentage of the responses are in the 50s and below?
What percentage of the responses are 60 or higher? What percentage of the responses are less than ? What percentage of the responses are at least 40 but below 70? What percentage of the responses are 65 or greater? What percentage of the responses are less than 35? What percentage of the responses are equal to 60? To determine whether a question can be answered, decide whether you have all the information you would need to answer it. Problem C2 For questions g and h in Problem C1, use the table to come up with an estimated percentage.
One assumption you might make is that each interval is divided evenly. So if the interval states that The relative frequency histogram looks similar to the frequency histogram; the only differences are that the labels along the vertical axis represent percentages, and the height of each bar now represents the relative frequency expressed as a percentage or proportion for the corresponding interval of values.
For example, the number of responses that are less than 60 is the cumulative frequency of If you begin with the stem and leaf plot for the 52 estimates of a minute, the 22 values in the lighter color are the estimates below Complete this cumulative frequency table with the information you collected from the histograms above:. Problem C4 Use only the cumulative frequencies from the table to answer the questions below. As with Problem C1, first determine whether a question can be answered using only this table.
How many responses are in the 70s and below? How many responses are 80 or higher? How many responses are in the 50s and below? How many responses are 60 or higher e. How many responses are less than ? How many responses are at least 40 but below 70? How many responses are 65 or greater?
How many responses are less than 35? How many responses are equal to 60? In This Part: Relative Cumulative Frequencies You can convert cumulative frequencies to relative cumulative frequencies by dividing each cumulative frequency by the total number of data values.
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