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

﻿Hello everyone, it's Mr. Miller here. In this lesson, we're going to be interpreting frequency tables. So, first of all, I hope that you're doing well, and we're going to start off with this data handling cycle again. Now over the last few lessons, we've been looking at analysing and processing our data. So finding things out, like the mean and the median, we also last time, looked at interpreting those results. And this time, we're going to be looking at representing the data. So it's important not just to analyse the data, to find some things out about it, but also to present it, to represent it in a way which is clear and accessible to people who are looking at our study. So let's go ahead and find out how we do that. Okay, let's have a look at the first question. Sam asks 25 students in his year group, how many siblings, brothers and sisters, they have? Here are his results. Represent the results in a frequency table. So what I want you to do, is I want you to copy down this table, use a ruler if you have one. And we're going to represent these results by having the number of siblings going from zero to six, and each time we get a result, so the first result is a one here, we're going to put a one in the tally next to one. The next one for two, we're going to put it next to two. So pause the video now and complete this for all 25 students. Have a go, couple of minutes, pause the video now. Okay, great, so I'm going to do this very quickly. And notice when I do this, I'm crossing off my results as I go so that I don't make a mistake. So another one here, a zero, a four, two twos, another one, a two and a three, a one and a zero. Now the next time I have a one, it's a fifth one. So I put a line through my results like that. Then a zero, a two, and a one, a three, three, six, one, two and a three, two ones, and finally a zero. Great, now that's done, I'm going to write in my frequencies. So for zero siblings, I've got four. For one sibling, well, this is five, and then six, seven, eight, nine. Then six, then four, one, zero, and one. Now what could I do to make sure that I haven't missed out a result? What could I do to check my answer? Well, notice how I know I've got 25 students here. So what I could do is I could add up my frequencies here to check that they sum to 25. So if I do that four plus nine is 13, plus six is 19, add the four is 23, and then the two ones gives me 25. So I can check my answer by adding up the frequencies. Okay, so this is how you represent these results in their their frequency table. And notice how it's much, much easier to see the results in the table than it is to see all the results just as numbers. And it's easier because I can see from the table that one sibling has got the most, and then followed by two, et cetera. Now, one more question, which is what is the mode and the range? Well, if you had the original data like this, you could go ahead and count all the numbers up to see which one is the most common, that would be the most. And then you could look for the biggest and the smallest to find out the range. But actually you can work out the mode and the range really easily just by looking at the frequency table we've already done. Have a think. What would the mode be and what would the range be looking at the frequency table? Well, to find out the mode, you need to look for the highest frequency, which in this case is nine. Now it's really important, nine is not the mode, the mode is actually one. Because one is the number of siblings that has come up nine times, it's come up the most. So the mode is one. And the range? Well, you're looking for the largest number of siblings, which is six, take away the smallest, which is zero, to get a range of six. So not only does a frequency table represent the data really clearly, but it also allows us to work out the mode and the range really, really easily. Okay, let's move on to the Connect task. Okay, these students are trying to imagine how many siblings there would be in total if everyone brought all their siblings into school. So the table is the same table as we saw on the previous slide, I just removed the tally 'cause we don't need that. The first student says, I would do zero plus zero plus zero plus zero plus one plus one plus one, et cetera. The other student says, I know a better way! So how could you use this table to work out the total number of siblings really, really quickly and easily? Well, you know that, for example, there are four lots of zeros. So zero times by four is going to give me zero. And you know that nine people have got one sibling. So the total number of siblings that that's going to give us is one times by nine, which is nine. What's the total number of siblings that come from the people with two siblings? Well, six people have two siblings each. So I do two times by six, gives me 12. What about the next one? Well, four people have three siblings each. So I do three times by four, gives me 12. The final one, four times by one gives me four. No one has five siblings, so that's going to be zero. And six times by one gives me six. So these are my total number of siblings that everyone has. So how do I find out the total number of siblings? Well, I'm just going to add them up all together. Nine plus 12 plus 12 plus four plus six, that gives me 21 plus 12 is 33. Gives me 43 siblings in total. So this is another use of a frequency table. It allows me, really, really easily to find the total number of siblings from the table. Okay, it's going to be your turn now, Independent task, let's have a look. Okay, let's read through this together. Leela asks a sample of 16 off a year how many bottles of water they drink per day? Here are her results. Put the following data into a frequency table and find the total number of bottles drunk, like we did on the Connect task, and the mode and the range. So you'll start off by copying down this table. The first column is going to be that number of bottles drunk, so zero one, two, three, four, you're first of all going to fill out the tally to get the frequency. And then you're going to find the total, the mode, and the range. Pause the video to complete this table and find out these things, should take you about four or five minutes. Pause the video now. Great, so you should have got for your tallies one, four, two, five, and four. And what you should have done is you should have added up those frequencies to make sure that they add up to 16, which they do. Now, let's find the total number of bottles drunk first. And I gave you this extra column here to help you to do this. So how do we do this? Well, the first one is going to be zero times by one is zero, then four people who drunk one bottle, so that's going to give me four bottles. Two people have drunk two, that's going to give me four. Five people have drunk three bottles, that will give me 15. And four people have drunk four, which is going to give me 60. So the total number, I'm going to add up four plus four plus 15 plus 16. Well, that's going to give me 39, and then the mode and the range. Well the mode, I'm looking for the frequency that appears the most, which is five. So the mode is going to be three. And the range is going to be four minus zero, which is equal to four. Great, well done if you got that. Let's move on out to the Explore task. Okay, Simon has asked 10 people in his class, how many pets they have, but he's lost two pieces of data. Here are the results that he has so far. So there are eight pieces of data there. However, he does know that with all the data included, the total number of pets is 20, and the mode is two. So what you need to do is fill out what you can of the table already and find out what the missing two pieces of data are. So first of all, get these pieces of data into your table and then using the information that the total number is 20 and the mode is two, see if you can find out the two missing pieces. Pause the video, copy down the table and have a go at this question. Okay, so well done if you had a good go at this. Let's first of all fill out what we know already. So the tally chart, I've got a zero here, got a five here, a one, a two, a zero, a one, a two, and a three. Okay, so those are my eight pieces of data that I've got so far. Now, let's have a look at this. The total number of pets is 20. Okay, what's the total number of pets already so far? Well, you could have a look at the original results and add them all up, or you could look at it from the frequency table, it's up to you. But if you add up all of these results that you have already, you get to a sum of 14. So what does that mean? Well, we know that the two missing pieces of data must add up to six. Okay, now we need to look at the fact that the mode is two. So if the mode is two, that means that two is the most common number. So we know that we have to have at least one more two, so I'll put that in a different colour for two to be the most. So I've added two there. Okay, so if I've added a two, what must the final piece of data be? Well, I know that the final piece of data must be a four because two plus four makes six. And this works because my mode is two, because that's come up three times, and all of my pieces of data now sum to 20. And I can even check that if I want to, by doing zero times by two, which is zero, and filling out the rest of these, and all of these numbers will sum up to 20. Okay, that is it for today's lesson, hope you've enjoyed it. Next time, we're going to be looking at frequency tables in more detail. So thanks very much for watching, and see you next time, have a great day, bye-bye.

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?

Interpreting Frequency Tables:

In this lesson, we will learn how to sort data into a frequency table.

Maths

Y8 Maths

Key Stage 3

Year 8

Interpreting frequency tables

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

Comparing data

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?

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

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:Interpreting frequency tables

Core Content

Univariate data: