The mean of the set of numbers 3, 3, 3, 4, 5, 6 is...

The median of the set of numbers 3, 3, 3, 4, 5, 6 is...

The mode of the set of numbers 3, 3, 3, 4, 5, 6 is...

The range of the set of numbers 3, 3, 3, 4, 5, 6 is...

Here is a set of numbers: 4, 5, 2, 1, 8. Tick the CORRECT statements

Statistics Lesson 7:

﻿Hello, everyone it's Mr. Millar here. In this lesson we're going to be comparing data. So first of all, I hope that you're all doing well. And we'll start again with this data handling cycle. Now over the last couple of lessons, we've been looking at step three of this data handling cycle, because we've been finding the mean, the median, the mode and the range, and that is all about processing the data, analysing the data that's come in. In this lesson we're actually going to have a look at step four of the cycle, interpret and discuss the results. So once we found things like the mean and the median, what does that actually mean? How do we interpret this? What does it mean for step one when we wrote our hypothesis? Does it support our hypothesis or not? So let's go ahead and look at the try this task. Okay, let's read this through together. Mr. Millar wants to see how many books student in his class read per month on average. He takes a sample and gets these results. He finds the mean. Comment on his result. Okay, so nice and straight forward. Find the mean of this eight numbers, and write a sentence or two commenting on this results. Pause the video for a minute to do this now. Great, so hope that you found this nice and straightforward. Find the mean, first of all. Well, as you know you add up all the numbers, and you should have got 48. I need to divide that by how many numbers there are, eight, and you get a mean of six. Hmm, what do you think? Does this fairly represents the results? Well, let me show you this in terms of a bar model. So the green bars represent the number of books that each student has read. The blue bars represent the mean, which we found out a moment ago is six. And as you can see all of these results that I'm circling now, they're all lower than the mean of six. So why is the mean six if most of the results are lower than six? Well, clearly it's because this result, the 27 has pulled up the mean. So if the 27 wasn't there, the mean would be a lot lower. Now, this is really important. We call this piece of data, the 27, an outlier. An outlier is a piece of data which is well outside the others. Having an outlier can skew the mean. So just take a moment to pause the video, to copy down this definition into your notes. Okay, great, so, well done for doing that. So an outlier is really, really important because if we have an outlier, then when we find the mean, it may not give us the most representative results. Instead of finding the mean, what do you think, something that we've learnt already. What do you think we could do instead that could give us a more representative result? Well, you could find the median, couldn't you? The median would be between the three and the four. It would be 3.5. And that would be, I think, a better representation of our results. It's the median is the number in the middle of the data, and it's not affected by the 27. So be careful. When you have an outlier, it can skew the mean. So you have to be aware of it. Let's move on to the connect task. Tim is deciding which bus to use to get to school, the 42 or the 61. He takes a sample of the time it takes in minutes for each bus to get to school. So six results for the 42, six results for the 61. Find the mean and range of each. Which bus would you recommend he take? So pause the video for two or three minutes. Find the mean and range of both of these buses, and write down a sentence saying which bus you think he should take. Pause the video now to give yourself some time to do that. Great, let's go through it then. First of all, the mean. The mean for the 42 bus was 126 divided by six equals 21. And the mean for the 61 bus is 120 divided by six, which is 20. So what does that tell you? Well, that tells you that on average, the 61 bus takes a shorter time to get to school. So if you were looking at that, you'd think, well, I like the bus that doesn't take me as long to get to school. So maybe I'll take that one. However, what about the range? For the first bus, it's 23 minus 20, which is three. And for the 61 bus, it's 44 minus six, 38. What does that tell you? Well, that tells you of course that the range for the 61 bus is a lot bigger. So the data is a lot more spread out. So which bus would you take to school? Well, if it were me, I would definitely take the 42 bus because even though the mean is a little bit higher, the range of times is a lot more consistent. So I'd know I'd be pretty confident that if I gave myself, you know, 23, 25 minutes to get to school, the 42 bus would get me there on time. Whereas the 61 bus, well, great. Some of the time it's really, really quick. It takes 10 minutes, eight minutes, great. But other times it takes me a lot longer, maybe because it's stuck in traffic, maybe because it takes a long time for it to come. I don't know. So what does this mean? It means that the range tells us about the consistency of results. So it's often worth paying attention to the range when you're making a decision like this. Okay, let's move on out to the independent task. Okay, great, so for the independent task, you need to find that mean, median, mode and range of these seven cards, and then find the mean, median, mode and range for these eight cards with the 55 included. So this first column, just the pink numbers. The second column with all the numbers including the 55. Pause the video to go ahead and do this now. Great, so you should have found that the mean was 15, and then it went up to 20 if you included the 55. The medium, well, that's going to be 14, with it not included. And then 14.5, if you did include it. The mode stays the same, and the range does change. It goes from 14 to 45. Okay, so let's just take a moment to pause here, and have a think about what's changed when we've added this 55, which is clearly an outlier. Which of this four measures have changed the most? Well, clearly as we saw earlier, the mean has gone up by quite a lot, hasn't it? And we saw that earlier, having an outlier skews the mean. What about the medium? Well, the median has only gone up from 14 to 14.5. So it hasn't really changed that much because the median looks at the middle of the data. So having one more piece of data, which is well outside the others, won't change it that much. The mode hasn't changed. That's usually the case, and the range has got a lot bigger because now the biggest number is significantly bigger than it was before. So the range has gone up by a lot. Great, let's move on out to the explore task. Okay, explore task, we've got six numbers, and in each of these, I want you to change one of the numbers to make the mode five, the median three, et cetera. So you're changing one of the numbers, each of these times to meet these conditions. This should be an interesting one. So pause the video five or six minutes to have a think, how many of these can you work out? Great, let's go through this. So the first one, make the mode five. Well, at the moment, there's only one five, isn't there? So we're going to have to make sure that we have another five. What's the mode at the moment? Well, it's three. So if you change one of the threes to a five, that works because now the mode is five, and that's definitely the mode because all of the other numbers come up only once. Hope you got that one pretty nice and straight forward. What about the median of three? Well, at the moment, the medium lies in the middle of these two middle numbers, so it's 3.5. How do we change it so that the median is three instead? Well, if we change this four to a three, then we can see that the median will lie between a three and a three. So it's going to be a three. What about the range as four? Well, at the moment the range is eight, isn't it? So we're going to have to change either the bottom number or the top number. And instead I found out that I need to change this nine at the top, I need to make that a five, because now the range is five minus one, which is four. If you had changed the one, let's say you'd made that a four or five. Now the range is nine minus three, which is six. So that doesn't work. You need to change the nine to a five. The final one was the trickiest. So well done if you wrote this up. You have to make the mean a five and keep the range four. How did you do this? Well, what I would do is I know that if the mean is five, and there are six numbers, the total is going to have to be five times by six, which is 30. And at the moment, if I do one plus three, plus three, plus four, plus five, plus nine, I get a total of 25. So I need to increase my total by five while keeping the range eight. So if I were to change the nine or the one, then my range would change. So I'm going to need to change one of the other numbers. For example, changing this three to an eight. Now my total has gone up by five. So my mean is now 30, but my mean is now five, sorry, but my range is still eight. Notice that you couldn't change the five to make it a 10, because that would raise that range to 10 minus one, which is nine. So that is it for today's lesson. Well done for completing it. Hope you enjoyed it and see you next time. Have a great day, and bye bye.

Here is a list of annual salaries at a company: £25,000, £25,000, £26,000, £26,000, £26,000, £27,000, £27,000, £28,000, £100,000. Why would the mean not be the most appropriate measure of average?

Samira asks a sample of her class their favourite colour. The results are: blue, pink, red, red, blue, pink, green, brown, red. Which of these averages would be the most appropriate to use?

Comparing Data

In this lesson, we will interpret differences between the mean, median, mode and range.

Maths

Y8 Maths

Key Stage 3

Year 8

Comparing data

Univariate data

Statistics and probability

THEME

UNIT

The data handling cycle

Forming and testing a hypothesis

Sampling

Survey questions

Finding the mean

Problem solving with the Mean

Median, Mode and Range

Interpreting frequency tables

Mean from frequency tables

Median from frequency tables

Interpreting bar charts

In the first 6 tests he takes, Jake scores a mean of 60 marks. In the final 4 tests, he scores a mean of 70 marks. What is his overall mean?

Looking at the table below, how many people had 2 pets at home?

Looking at the table below, what is the mode number of pets?

Looking at the table below, what is the range number of pets?

Looking at the table again answer the following question. If everyone in the survey brought their pets to the park, how many pets in total would there be?

Which of these is the first stage in the data handling cycle?

A student asks her classmates how many brothers and sisters they have. What best describes the type of data she collects?

In order to test what Arsenal fans think about their manager, a student gives an online questionnaire to 100 Arsenal fans. The student is testing his hypothesis by taking a ….

Mr Millar wants to test whether people prefer reading books to watching TV by asking 300 people outside Waterstones (a book shop chain) on a Friday morning. What is the most likely reason that this sample will be biased?

A set of 5 numbers is 3, 7, 8, 10, x (where x is a missing number). The mean of these 5 numbers is 6. What is the value of x?

Mr Millar is surveying a group of people about their reading habits. One of the questions is: "Reading is good for you. How many books have you read over the last year?" What is wrong with this question?

Lesson overview:Comparing data

Core Content

Univariate data: