﻿Hi, welcome to our fourth lesson in the percentage and statistics unit. Today we'll be learning to calculate the mean as an average. All you'll need is a pencil and piece of paper. So, go and get your things if you haven't done so already. In today's lesson, we're calculating the mean as an average, we'll think about averages. We'll look at a formula for calculating the mean. We'll find missing values using the mean. And then we'll move on to some independent learning and then a final knowledge quiz. So, let's start off by thinking about averages. You may have seen these different types of averages before. So, we've got the Mean, which is a calculated average. The median, where you calculate the middle value of a set of data. The Range, where you look at the difference between the greatest and smallest values. And then, the Mode and the mode is the most common value in a set of data. Today, we're going to work on the mean, which is a calculated average. So, let's start by looking at the question together. Five friends record the number of goals they scored during a football tournament. And each of these purple squares represents one goal. We want to know what is the average number of goals they scored. So Fran, you can see scored five goals. Jenlya scored seven, Zack score four, Jannah eight and Ra-eesa six. And we're looking for the average. So, now I've got the number of goals and I've taken the names away and I've just got the goals still here. And what I need to think about is, how many goals have been scored all together? And I've added that up and it's equal to 30. So altogether, the five friends scored 30 goals. Now, when I'm thinking about the mean, I'm thinking about what if they scored an equal amount of goals? What if these goals were spread out equally between the five friends? How many would they have scored each? So, now I'll bring my names back and I've assigned an equal number of goals to each of them. So, that means that they each scored six goals, okay. So on average, each of the five friends scored six goals. And I calculated that, by taking the number of goals in total which was 30 and dividing it by the number of friends, which was five. And that gives me the average number of goals. 30 divided by five is equal to six. Let's apply this thinking to another question. So in January, 2017, six Astronauts were aboard the International Space Station. And their ages were shown here in this table. Now, what we want to know, is what is the mean age of the astronauts on the International Space Station? And how might this be calculated? So, we need to think about what is their age in total? What is the total number of years that those people have lived for? And then we're going to share it out equally between the six people onboard. So, this is what it will look like. We're adding each of these ages up together, which gives us a total of 282. And then we're going to take this combined age and share it equally between the six astronauts. So, that will be 282 divided by six, which is equal to 47. So, the mean age of the astronauts is 47. So, let's look at this in terms of a formula. To calculate the mean, we sum all of the data points and then we divide it by the number of data points. So, in the previous one, we added the ages. We found the sum of all the data points and we divided it by the number of data points, which was six, because there were six people and that gave us the mean. So, now you have a formula to work with. I want you to approach this question independently. So, I'll read it to you and then you can pause it. A new astronaut joins the team. She is 40 years old. So, here is your original six and their ages. You've got one more and her age is 40. So, I want you to calculate the mean average and see if it has changed. Pause the video now and calculate the mean. So, now in order to find the mean age we needed to add up all of the ages, including the new person, which gives us a total of 322. Now, this time we're dividing it by the number of data points, which is not six, that's seven because we have a new person joining the team. So, 322 divided by seven is equal to 46. So, the mean average did change. It went down by one year. So, this new astronaut, brought the mean age of the astronauts, going to the International Space Station down by one year. So, that's calculating the mean. Now, we're going to look at calculating missing values using the mean. So, here we have a number line and the arrow shows the mean of a set of four numbers. So, if you think back to our formula, we've got the sum of the numbers divided by how many there are, how many sets of data. So, it's going to be four that we're dividing by. Now, three of the numbers in the set are marked with dots, but one is missing. And we need to work out what the fourth numbers is. So, we'll do one together, then you'll have a go do one independently. Now, we need to determine, what the known numbers are below the red dots. So, we can use our knowledge of calculating scales and determine what value of each of these red dots is. So, this one's halfway between four and six. So, that must be five, halfway between six and eight is seven and halfway between 10 and 12 is 11. The other thing we need to determine is what this arrow is pointing to, which is halfway between eight and 10 and that's nine. So, the mean of the dataset is nine. So, now what do we know? We know that the mean of four numbers is nine and we know three of those numbers, so we can write it like this. We know that, five plus seven plus 11 plus something unknown divided by four because there are four datasets is equal to nine. So, now we need to figure out, what is the missing number. We know that the sum of the four numbers in the set divided by four equals nine. So, we have to think what divided by four equals nine and we can use the inverse, where nine times four is 36. So, these four numbers must be equal to 36 when added together. So, we know that these numbers five plus seven plus 11 plus something equals 36. And we can work out the missing number by adding these three together and subtracting 36. And that gives us a missing data piece of the team. So, now I want you to use the same logic to work out the missing number in this data set. So, now we have a blue arrow pointing to the mean, which is nine. And there are five numbers in the set. What is the missing number in this dataset? Pause the video now and find the missing value. So, we know that if the mean is nine, which is what the arrow is pointing to on the number line, then the sum of this dataset must be divided by five to equal nine. So, we think what divides by five to equal nine. Well, we can use the inverse, nine times five equals 45. So, these numbers must add together to equal 45. And if you add those numbers up together and subtract them from 45, you'll find that the missing number that you were looking for, was nine. Now, it's time for you to complete some independent learning. So, pause the video and complete the task and then click restart once you're finished. So, for question one, you had three sets of data and we're asked to calculate the mean. So, for set one, you were adding up the values and dividing them by eight because there are eight numbers in total. The numbers added up to 24. So, 24 divided by eight is equal to three. So the mean of set eight is three. For b again, add up the data and divide by eight because there are eight values. The data adds up to 80, 80 divided by eight is equal to 10. So, the mean of set B is 10. And C adding them up. And this time dividing by seven, because there were seven pieces of data and they added to 203. And now divided by seven is equal to 29. So, for question two, you had pupils running a 100 metre race, a 100 metre hurdle and 100 metre sack race. And you were asked first of all, to calculate the average time for each race. So, we'll start with the 100 metre race. So, you were adding up all of the values and dividing by the number of people running, which was one, two, three, four, five, six, seven, eight. And it should look like this. So, all of these added together is equal to 174 divided by eight, gives you an average of 21.75 seconds for the hundred metres. For the a hundred metre hurdles. Again, adding them together and dividing by eight gives us an average of 29.875 seconds. And the sack race, that one added up to 278, which means that the average time was 34.75 seconds. So, the slowest race was the sack race. Part b, you were asked to calculate the average time for each person to complete all three races and give your answer to the nearest second. So, starting with Elizabete 20 plus 28 plus 31 divided by three is 26.3 seconds. And to the nearest second, that rounds to 26 seconds. For Kyra it was 26.3 recurring as well, which gives us an average of 26 seconds. For Omar, his average time was 27.6 recurring, which is equal to approximately 28 seconds when you round it. Sarah, her average is 32.6 recurring, which rounds to 33 seconds. Yassar, it was also 26.3. the same as the top two, which is approximately equal to 26 seconds. For Rownel, his average time is 27.6 recurring, which is approximately 28 seconds to the nearest second. Liman, his time was nice tidy divide that came to 36 seconds And Mariam, 27.3 recurring, which is approximately 27 seconds. For question three, you were asked to tell me, what the three numbers could be that have a mean of 10 with all three numbers being different? So, what we're saying here is that, something plus something plus something divided by three equals 10. So, we know that the sum of these three numbers must be 30, because 30 divided by three is equal to 10. So, your solution is any three numbers that add up to 30. And I couldn't possibly go through every combination. So, as long as your three numbers total 30, then that will be the correct answer. For question four, you have three out of four numbers in a dataset that have a mean of six, and you were asked to calculate the missing number. So, this is how you could have set out, three plus five plus something plus nine divided by four is equal to six. So, we know that these numbers must add up to 24, because 24 divided by four is equal to six. So, then we thinking 17 plus something is equal to 24. The missing number, therefore must be seven. 17 plus seven is 24 and 24 divided by four is equal to six. In your final question, we've got a scenario where Janiya buys two adult tickets and two children's tickets for the theme park. The adult tickets cost 45 pounds each and the children's tickets cost 27 pounds each. So, you asked, what is the mean cost of the tickets? So, first job is to work out how much was spent on the tickets all together. So, that's two lots of 45 pounds and two lots of 27 pounds. So, you could just set it out either as repeated addition or as a multiplication using brackets. And then, you have four data sets. So, you're dividing your answer by four to give you the mean. So, those numbers all together is 144. She spent 144 pounds on tickets and divided by four is equal to 36. So, the mean cost of the tickets is 36 pounds. Now, it's time for your final quiz. So, pause the video and complete the quest and then click restart once you're finished. Excellent work today six, in our next lesson, we're going to be learning to interpret line graphs. I'm looking forward to seeing you then.

Calculate the mean of the data set below.

The data below shows the amount of time 6 pupils took to read one chapter of a book. Calculate the mean time taken to read the chapter, giving your answer to the nearest minute.

The mean of the five number cards below is 9. What is the missing number?

Interpret Mean as an Average

In this lesson, we will explore averages before creating a formula for calculating the mean. We will then move on to find missing values using the mean.

Lesson overview:Interpret Mean as an Average

Core Content

Percentages and statistics: