In this video, we will look at frequency distributions. We will look at frequency, relative frequency, and cumulative frequency. First, let's start with some definitions. So, for looking at all different types of frequency distributions, we have a basic frequency distribution that lists each category and the corresponding number of occurrences. Please note that frequency distributions can be used for both qualitative and quantitative data. The relative frequency is the ratio expressed as a fraction, percent or proportion of the number of times a value of the data occurs to the total number of outcomes. So to find the relative frequency, all we have to do is take each frequency and divide by the total number of outcomes. If we want a cumulative relative frequency, we really want a running total of the relative frequency. So this is the accumulation of the previous relative frequencies. To find this, we only have to add all the previous relative frequencies to the current relative frequency. Let's look at an example. In this example, a phabotamist draws blood on a random sample of 30 patients and records their blood types as shown. So looking at the table, it looks like we have blood type O, A, B, and AB. So noticed in that first column under blood type, those are the only blood types that we list. To get the frequency, relative frequency, and cumulative frequency, we'll take that one by one, and I'm going to express it in one table, and you can do the same thing in the homework. So to get frequency for blood type O, we need to count up all the different O's that we have. Looks like we have 11 O's. So I'll enter that into that frequency. And then to get the other frequencies for blood types A, B, and AB, we do the same. So for A, it looks like we have 11. For B, it looks like we have five. And for AB, we only have three. to calculate the next column, the relative frequency. Remember, relative frequency is the frequency divided by the total outcomes. In this case, we have a random sample of 30 patients. So, I'm going to divide each frequency by 30. For blood type O, we take 11 / 30 and get.37 when we put in our calculator. This is a rounded value, so two decimals is fine unless it's otherwise stated. And then we'll do the same for blood type A. Again the frequency is 11. So we'll divide by 30 and get another.37. For blood type B we have 5 / 30 which is.17. And the last blood type A is 3 for a frequency divided by 30 and we get 0.1. To complete the last column our cumulative relative frequency we are going to make a running total. So our first row has nothing to add but that first relative frequency. So we'll just enter 37. To get the next row, we need to take our 37 from blood type O and add it to the fre relative frequency for blood type A. So we have 37 plus another 37 and we get 74. Now we can use that running total to help us. So we now have a running total of 74. So we'll add that to our next blood type B which is 0.17 and get 0 91. And then lastly we're going to take the 0.91 add it to our very last blood type of 0.1 and we get 1.01. Now remember relative frequency is really a proportion decimal or percent. So if we're taking a cumulative relative frequency, we really want that very last entry to be close to one or 100%. In this case, because we rounded, it's okay that it's a little bit off. So don't be worried if you get a little bit above one or a little bit below one. Let's look at another example. In this example, the data shows the number of televisions in a random sample of 40 selected houses. So, we're going to answer a few questions here. First question, are these data discrete or continuous? So, because we're answering about the number of televisions in our household, this is actually going to be discrete because remember discrete means we have gaps. So, we couldn't answer 2.3 or 2.5 televisions. It has to be a whole number. The next question asks us to construct a frequency and relative frequency distribution. Just like the other example, I'll do this all in one table. Looking at the data, it looks like we have entries of 0 1 2 3 4 and five televisions. So that will make my first column. And now we just need to add those up. So looking at the frequency for zero TVs, it looks like only one household entered zero. So we'll put one there. Now we're going to count up the number of people who had one television. Looks like 14. Counting up the number of households that reported two televisions looks like 14 again. For three, looks like we have eight people. four televisions, we have two people who reported that. And for five televisions, it only looks like we have one. For the relative frequency, we're going to take each frequency and divide by the total number of outcomes. Again, in this case, our total number of outcomes is 40. So, I'll take each frequency, in this case, zero TVs, we had frequency of one, and divide it by 40. That gives us 0.025. And we'll continue this for all the other televisions. So a frequency of 14 divide by 40 we get.35. Do that again we get another.35. For three televisions we reported 8 as a frequency. So we'll take 8 / 40 get2 and we'll continue on for four televisions and five televisions. Now, the last question asks, what percentage of households have four or more TVs? Now, four or more doesn't just mean four or five. We actually have to take both of those because we could have four televisions or five televisions, and that would be okay. To do this, we're going to add up our relative frequencies. So, looking at the number of televisions for four, it looks like we have a relative frequency of 0.05. 05 and five televisions we have a relative frequency of 0.025. So we'll add those up because again four or five TVs would satisfy this question. Now the only other thing we have to do is we have to convert this to a percent just because they asked what percentage of households. So right now we have it as a decimal. All we need to do is move the decimal over two places and we will have our percentage. So, it looks like 7.5% of households actually have four or more TVs.