 The first lesson of JSE Mathematics in a series of two lessons. The topic of this lesson is statistics. The objectives of this lesson are to do a survey to collect data. Use collected data to draw a pie chart. Let's switch over to hear what Jason and Susie are doing to get info about the most popular chocolate to sell at their tax shop. I don't know how you can swallow the thing that you're eating. Those nuts are enough to cure me from chocolate forever. You don't know what you're missing. Don't you think it would be boring if we all liked the same thing? What's your favorite chocolate, by the way? I like the plain white chocolate. It just melts in your mouth. Hey, before you get to carry it away, you should start thinking of what kinds of chocolate we want to sell at our tax shop next year. Yeah, now that you mention it, how will we know what the most popular chocolate is amongst our things? There should be a way. Let's go to Ms. Thompson after school and ask for her help. Yeah, that's a great idea. Let's see you after school. Yeah. Anyway, I still need to go to the library, so I'll see you after school. Okay, ciao Jason. Bye. Bye. After school? Okay, Jason. Bye. This is the price. You must have a serious problem when you come to me after school. Yesterday, we needed to do something about it. So we thought we should cover some rules of your help. Sure. So have a seat and maybe you can tell me how I can help. Sure. Thanks very much. You see ma'am, we have to start running the tax shop soon. So we would like to buy chocolates to sell. And we don't want to buy eight different kinds of chocolate and not know which one is the most popular and which one is the least popular. Amongst our friends. Yes, even Susie and I like different kinds. What we want to know is how we can find out what the most popular chocolate is amongst the students. So what you actually want to do is collect data. Collect what? Data, Jason. It's just another word for information. Oh, I see. So how do we collect the data ma'am? I'll show you. Have you identified the certain types of chocolates that you want to find out about? Yes ma'am. We've already made a listing table for you. Here it is. Okay. What I can see from the list is that you have identified certain kinds of chocolates like white, nuts and mint and so on. So you want to find out how many people like these kind of chocolates? Yes ma'am. Spot on. Good. Now I'll show you how to prepare a form to do a survey and to collect data. Once you've done this, you can come back to me and we can go from there. That sounds good ma'am, but how do you prepare the form? Draw a column on the right hand side of the list like you've already drew. The students can then take their to show their choice of chocolate. Above this table, write down the question you want to ask. I guess we want to know what their favorite chocolate is. That's right. So I'll put that question in. That's great. Now you need to make a lot of copies of this form and ask the students to fill it in. Once you've gotten all these copies back, you must make a summary by counting the data and using telemarks. What are telemarks ma'am? Let me show you. Many people like white chocolate. Two like chocolate with nuts and five like mint chocolate. Now we are going to transfer the data to a frequency table and show the information using telemarks. Telemarks is just an easy way of counting a lot of data by drawing bundles of five. You draw four vertical sticks and the fifth stick is drawn horizontally. This is a bundle of five. What does frequency mean ma'am? It is the word we use in statistics to indicate how frequently or often an item appears. Gee, thanks ma'am. We'll do the survey tomorrow during break and we'll come back to you as soon as we've collected all the data. Okay you guys, have a nice day. Bye. Bye. Bye. Come in. Good afternoon to you. So how did it go? I would say great. Yeah, me too. That's nice of you. So Danny, show me what you've done. Show me what you've done. Whoa, you've done a great job. Well done you guys. Thanks ma'am. Last time you told me you wanted to know what type of chocolate is the most popular. Now it's very easy to see. Is there something else you want to do with the data? Yes ma'am, while we were doing the survey we thought it would be a great idea to show the students which chocolate is the most popular and which is the least popular amongst them. Yes, we want to put it up in the talk show. I think that's a great idea. There are a lot of ways to illustrate data. But I will show you how to display data on a pie chart. A pie chart? Yes, it's a circle with sectors of different sizes to show your data. But let me not jump the gun. Let's start from the beginning. We have to draw a circle. So you would need your compass for this. You also need your protractor because we are going to measure angles as well. Hope you've got them here. Remember your calculators too. Yes ma'am. Mine is always with me ma'am. Great. Let's start by drawing a circle. Make your radius 3 cm. Because there are 8 different kinds of chocolate, we will have 8 sectors inside the circle. But we don't know what size they will be. So we must first calculate the size of each sector. How many degrees are there around the center of a circle? I know. Yes, you're right. So we must find out which part of the 360 degrees is occupied by each kind of chocolate. Does that make sense to you? Yes ma'am. But how do we find the angle? First of all, I need you to tell me how many people took part in your survey. It was 120 ma'am. Good. You have 8 different kinds of chocolate, right? Take your data sheet and take the first chocolate. How many letters chose white chocolate? It was 20 ma'am. Okay. So 120 light white chocolate. Now, we just multiply the fraction 20 over 120 by 360. What is your answer? Okay, let's think about it. We know that 20 out of 120 chose white chocolate. And we want to see this fraction as part of the whole part. We can write down the fraction 20 over 120 and next to it to a fraction out of 360. We want these two fractions to be equal. Can you see how to do this? Well, I want to say that 360 is 3 times bigger than 120. That's good. So what would the numerator of this fraction be? It must be 6 since the denominator has increased 2 times the numerator must be equal to 60. Excellent. But it's actually 60 degrees because we are working with angles. Can you see another way of doing the same calculation? I was thinking that you can multiply the fraction 20 over 120 by 360 degrees. That gives an answer of 62. Right. Now go back to the circle and draw any radius inside the circle. Take your protractor and measure an angle, 60 degrees and complete the angle and label it once. Now, Jackson, let me see if you can do the next one. How many people chose last? It was 30. So, 50 out of 120 liked last. What was I doing now? Susie, can you help him? You can write 30 out of 120 multiplied by 360 degrees. Of course, the answer is 90 degrees. I've noticed that 90 is 3 times 30. So each time we need to multiply the value from the table by 3 to get the angle of the center in degrees. Good. You draw the next angle and label it. Susie, how about the next one? How many people chose last? It was 15 men. So it's 15 over 120 multiplied by 360 degrees and the answer is 45 degrees. Well done. I think you got it now. You can draw your pie chart on a big poster and make sure each center has its color. It will attract a lot of people's attention and your sales will improve. Thank you so much, Mrs. Thompson. You've been a great help to us. At that point, what is your favorite type of job? I like the plain brown ones. You get more chocolate for your money. No nuts, no other stuff to spoil it. Don't remember that, man. Thanks a lot. See you tomorrow, man. Okay, you guys. Have a good day. Bye. A pie chart is an easy way of counting a lot of data by drawing bundles of five. Frequency indicates how often an item appears. A pie chart is a circle with sectors corresponding in size to the data involved. Let's recap how to calculate the different sectors of the pie chart. We take the frequency from the results table and divide that amount by the total number of results and multiply with 360. For example, for brown chocolate the frequency is 10 and its sector is 10 divided by 120 multiplied by 360 which gives you 30 degrees. You can check your answer by multiplying each of the values from the frequency table by 3 to get the angle of the sector 2. Here is a summary of the calculation of all the sectors of the pie chart. Now let's have a look at the complete results on the pie chart. According to the results the most favorite chocolate flavor is the nut flavor. I think with all these results Susie and Jason will be able to make sure they buy enough stock of the most popular types of chocolate for the tuck shop. This brings us to the end of today's lesson. The next lesson in our series on JSE Mathematics will deal with line graphs. Goodbye.