1. 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

2. 1. Doing a Survey!

3. 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!!!

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

5. 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.

6. 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!!

7. 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

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

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

10. 2. Collecting Data

11. 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.

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

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

14. 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

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

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

17. 3. Representing Data

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

20. Pie Charts

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

22. 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.

23. 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.

24. 4. Finding the Average, Mode and Median

25. 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.

26. 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

27. 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.

28. 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.

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

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

31. 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.
= 183
183 ÷ 2
The median is
91.5

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. 5. Using Spreadsheets

41. 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

42. 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.

43. The Microsoft Excel Screen

44. 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.

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

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

47. 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

48. There it is: