4. Finding the Average, Mode and Median 1. Doing a Survey 2. Collecting Data 3. Representing Data 4. Finding the Average, Mode and Median 5. Using Spreadsheets

1. Doing a Survey!

You’ve watched two hours of TV everyday this week Jack You’ve watched two hours of TV everyday this week Jack. It would be better to use this time for something more educational!!!

Everybody else watches the same as I do! Let me show you that I am right!

What do you comment about these questions? The meaning of ‘a lot’ could vary depending on the person asked. The second question should perhaps say ‘… do you watch most’ or ‘… do you prefer’. The set of responses does not include enough categories. Also it should be made clear whether more than one box may be ticked.

Ok! I will change the questions accordingly. Students should realise that 15 people is not a large enough sample for the results of the survey to be meaningful. They should also realise that Jack should not just choose his friends – he should use a method of random selection. Ok! I will change the questions accordingly. Then, I will ask 15 of my friends in my class!!

Explain what is wrong with each question Question 1: not enough possible responses given Question 2: £2 appears in two possible responses no box for between £5 and £10

Explain what is wrong with each question Question 3: responses not mutually exclusive Question 4: biased question

Write survey questions Now it’s your turn to write a questionnaire to find out more about an assigned topic.

2. Collecting Data

Collecting Data Statistics Raw Data A branch in mathematics where we collect, analyse and interpret data. Raw Data Disorganised information. This is collected through surveys, experiments, and observations.

Frequency Table (Tally Chart) Hobby Tally Frequency Play Sports (S) Play Games (G) Read a Book (B) Watch TV (T) Internet (I) Other (O)

Hobby Tally Frequency Play Sports (S) Play Games (G) Read a Book (B) Watch TV (T) Internet (I) Other (O)

Hobby Tally Frequency Play Sports (S) l l l l l l l Play Games (G) l l l l l l l l Read a Book (B) Watch TV (T) Internet (I) l Other (O) l l l l

Collection of Data Revision Raw Data Disorganised information Frequency Table Organise information in a table 3. Tallying Display information in groups of 5’s

How could we make the information presented in a frequency table much easier to understand and interpret? (Discuss in pairs)

3. Representing Data

Hobbies in our class Scale Title Bars Frequency Labelled Bars Labelled Axes

Pie Charts

Which mode of transport do you use to go to work?

Pie Charts We use pie charts to represent information, when some quantity is shared out and divided into different categories. The size of the pie slice (sector) represents the size of the group.

Pie Charts The size of the pie slice is given by the size of the angle at the centre. Therefore, to construct the pie chart we need to find the size of the angles. To find each angle, we write each group as a fraction of the total and multiply it by 360o.

4. Finding the Average, Mode and Median

What is the MEAN? How do we find it? The mean is the numerical average of the data set. The mean is found by adding all the values in the set, then dividing the sum by the number of values.

Lets find Abby’s MEAN science test score? + 97 Lets find Abby’s MEAN science test score? 84 Add all the values. 88 100 95 63 Divide the sum by the number of values. 73 86 783 9 ÷ 97 The mean is 87 783

What is the MEDIAN? How do we find it? The MEDIAN is the number that is in the middle of a set of data Arrange the numbers in the set in order from least to greatest. Then find the number that is in the middle.

63 73 88 95 84 86 97 97 The median is 88. 100 Arrange values from least to greatest. 63 100 73 88 95 97 84 86 97 Find the number that is in the middle. The median is 88. Half the numbers are less than the median. Half the numbers are greater than the median.

Think middle when you hear median. Sounds like MEDIUM Think middle when you hear median. large medium small

How do we find the MEDIAN when two numbers are in the middle? 1. Add the two numbers. 2. Then divide by 2.

There are two numbers in the middle. Arrange values from least to greatest. 100 63 88 95 97 73 84 97 There are two numbers in the middle. Add the 2 numbers. Divide by 2. 88 + 95 = 183 183 ÷ 2 The median is 91.5

What is the MODE? How do we find it? The MODE is the piece of data that occurs most frequently in the data set. A set of data can have: One mode More than one mode No mode

The value 97 appears twice. Arranging values from least to greatest makes it easier to find the mode. 63 100 73 88 95 97 84 86 97 Find the number that appears more or most frequently. The value 97 appears twice. All other numbers appear just once. 97 is the MODE

MODE MODE MOST OFTEN Most Often A Hint for remembering the MODE… The first two letters give you a hint… Mode Most Often MODE MOST OFTEN

Which set of data has ONE MODE? 9, 11, 16, 6, 7, 17, 18 A B 18, 7, 10, 7, 18 C 9, 11, 16, 8, 16

Which set of data has NO MODE? 9, 11, 16, 6, 7, 17, 18 A B 18, 7, 10, 7, 18 C 13, 12, 12, 11, 12

Which set of data has MORE THAN ONE MODE? 9, 11, 16, 8, 16 A 9, 11, 16, 6, 7, 17, 18 B C 18, 7, 10, 7, 18

What is the RANGE? How do we find it? The RANGE is the difference between the lowest and highest values. largest number smallest number - RANGE

Arranging values from least to greatest makes it easier to find the RANGE. 97 63 95 97 73 86 88 84 Subtract the lowest value from the highest. 97 63 34 34 is the RANGE or spread of this set of data

5. Using Spreadsheets

What is a spreadsheet? A spreadsheet is software which is used to work out calculations. For example, spreadsheets can be used by: a tuck shop to keep track of his stock or to keep a list of sold items the school to keep class lists the teachers to keep the marks students obtain in home works and tests

Why do we use spreadsheets? Calculate data: Many spreadsheets come with built-in formulas that can be used to calculate data. Some of the commonly used built-in formulas include those for addition, subtraction, multiplication, finding the maximum, finding the minimum, average, etc. Analyse data: Spreadsheets make data easy to analyse. Present data: Spreadsheets are able to make data easy to analyse through the use of charts and graphs.

The Microsoft Excel Screen

Formulas in Excel A formula is used to do every single calculation in the spreadsheet. A formula can be as simple as adding up two numbers in different cells or it can be as complex as working out a statistical result from millions of pieces of data collected over months.

To use formulas in Excel: Step 1: Enter the Data Step 2: Add the Equal (=) Sign Step 3: Add Cell References

Creating graphs in Excel Consider the following data: Now we need to present this in a graph – let’s do this!!

Steps Required: Highlight the data that you want to plot Go to Insert Choose the type of graph required, which in this case is a Pie

There it is: