2. This week: Data and averages
Name and describe key data collection vocabulary, including data types
Name and describe types of sample
Explain characteristics of a good hypothesis
Calculate the mean, median, mode and range
Calculate averages from sets of data, frequency tables and bar charts

3. crayons ate dad (2 words)
Anagrams
adat arc poem pithy shoes
a pyramid art (2 words) true oil
crayons ate dad (2 words)
I tint aqua vet scout union
tequila vita secret ID
maples cussen
continuous data sample compare quantitative hypothesis census primary data outlier secondary data qualitative discrete

4. Answers adat arc poem pithy shoes data compare hypothesis
a pyramid art true oil
primary data outlier
crayons ate dad
secondary data
I tint aqua vet scout union
quantitative continuous
tequila vita secret ID
qualitative discrete
maples cussen
sample census

6. Discrete vs continuous
Count it or measure it?
Examples?

7. How many cows are there in that field?
Discrete
Continuous

8. How fast can your car go?
Discrete
Continuous

9. How much water is there in this bottle?
Discrete
Continuous

10. How many CDs do you own?
Discrete
Continuous

11. What is your shoe size?
Discrete
Continuous

12. How much does a whale weigh?
Discrete
Continuous

13. How much does a Mars Bar cost?
Discrete
Continuous

14. What is the temperature of this fire?
Discrete
Continuous

15. How long does the bus to Birchington take?
Discrete
Continuous

16. How many goals have you scored this year?
Discrete
Continuous

17. Discrete Qualitative Continuous
What is the breed of that dog?
Discrete
Qualitative
Continuous

18. Hypothesis A good hypothesis is a statement, NOT a question
A good hypothesis can be tested
Is this a good or a bad example of a hypothesis? If bad, how could you change it to make a good hypothesis?
In tubes of Smarties there are always the same number of each colour.

19. Are these good or a bad hypotheses
Are these good or a bad hypotheses? What needs to change to improve the bad hypotheses?
Do you always get the same number of crisps in a packet?
Goldfish can read books.
Can you survive a bite from a shark?
Exams are getting easier.
January is warmer than February.
Adele is more popular than Madonna.
The music from the 1980s is the best.
The most popular subject at school is maths.

21. Choosing a sample
Usually, the population is too large to survey all of its members.
A small, but carefully chosen sample can be used to represent the population. The sample must reflect the characteristics of the population from which it is drawn.

22. There are two questions to be asked about a sample:
How big does the sample need to be?
How is a sample taken so that it represents the population accurately?
Sample size can vary but usually the larger the sample, the more reliable the results.
A new canteen is going to open at the college.
The canteen manager wants to find out what students would like on the menu. He decides to ask the students.
What population should he use?
Describe how to choose the sample.
Give one advantage and one disadvantage of him using a census.
An estate agent wants to get information about house prices in the city where she works.
What is the population she will use?
Why would she not use a census of the house prices?
She decides to use a sample. She also decides to use the prices of all houses on her list of houses for sale.
Give a reason why this might be a poor sample.

23. Discuss whether this will form a satisfactory sample for the poll.
A market research company is going to do a national opinion poll. They want to find out what people think about the European Union. The company is going to do a telephone poll.
First they will pick 10 towns at random.
Then they will pick 10 telephone numbers from the telephone book for each town.
They will ring these 100 telephone numbers.
The people who answer will form the sample.
Discuss whether this will form a satisfactory sample for the poll.

42. The mean is calculated by adding up all the values and dividing by how many there are.

44. HOMEWORK
How can we find the mean, median, mode and range from the frequency table?
Score 1 2 3 4 5 6
Tally
What is wrong with just adding all the frequencies and dividing by six ?

45. How can we find the mean, median, mode and range from our bar chart?
HOMEWORK
How can we find the mean, median, mode and range from our bar chart?
Can we find the mean and median without writing anything down?

46. This bar chart represents the scores that were obtained when a number of people entered a penalty-taking competition. Each person was allowed six penalty kicks.
How many people entered the competition?
How can you tell?
How can you calculate the mean, median and modal number of penalties scored?
What proportion of the people scored one penalty?
What is that as a percentage?
What proportion scored three penalties? Six penalties?
Can you think of another type of statistical diagram that can be used to show proportions?

47. Heights of 10 students:
175cm; 154cm; 198cm; 145cm; 134cm; 156cm; 156cm; 167cm; 145cm; 156cm Calculate the mean, median, mode and range of this set of data.

48. ABC Motoring
Here are the number of tests taken before successfully passing a driving test by 40 students of “ABC Motoring”
Number of tests taken
Number of People 1 9 2 11 3 7 4 6 5
2, 4, 1, 2, 1, 3, 7, 1, 1, 2, 2, 3, 5, 3, 2, 3, 4, 1, 1, 2, 5, 1, 2, 3, 2, 6, 1, 2, 7, 5, 1, 2, 3, 6, 4, 4, 4, 3, 2, 4
It is difficult to analyse the data in this form, so group the results into a frequency table.

49. Finding the Mean Number of tests taken Number of People 1 9 2 11 3 7 4
When finding the mean of a set of data, we add together all the pieces of data
Number of tests taken
Number of People 1 9 2 11 3 7 4 6 5
This tells us that there were nine 1’s in our list. So we would do:
= 9
(It is simpler to use 1x9!!)
We can do this for every row.

50. Number of tests x Frequency
Finding the Mean
Number of tests taken
Number of People 1 9 2 11 3 7 4 6 5
Number of tests x Frequency
1 x 9 = 9
2 x 11 = 22
3 x 7 = 21
4 x 6 = 24
5 x 3 = 15
6 x 2 = 12
7 x 2 = 14
We now need to add these together
So we have now added all the values up. What do we do now?
We divide by how many values there were.
So we divide by the total number of people. 40
107
107 ÷ 40 = 2.7 (1dp)
Students who learn to drive with ABC motoring, pass after 2.7 tests.

51. Bob’s Driving School
Now let’s look at another Driving school from the same town. Here are the number of tests taken by 40 students at “Bob’s Driving School”
3, 2, 4, 1, 3, 2, 3, 1, 2, 1, 2, 4, 4, 4, 5, 2, 3, 4, 3, 4, 4, 5, 5, 2, 3, 2, 4, 5, 3, 3, 4, 3, 2, 2, 2, 2, 4, 3, 3, 3
Grouping the data will help us to analyse it more efficiently…

52. Number of tests x Frequency
Bob’s Driving School
Number of tests taken
Number of People 1 3 2 11 12 4 10 5
Number of tests x Frequency
1 x 3 = 3
2 x 11 = 22
3 x 12 = 36
4 x 10 = 40
5 x 4 = 20 40
121
121 ÷ 40 = 3.0 (1dp)
Which of the two driving schools would you choose? Write two sentences to say why.
Students who learn to drive with Bob’s Driving School, pass after 3.0 tests.

53. Mean = 2.7
Range = 6
Mean = 3.0
Range = 4

54. Mean from a Frequency Table
The number of goals scored by Premier League teams over a weekend was recorded in a table. Calculate the mean, median, mode and range.
Frequency
Goals 2 1 4 2 8 3 3 4 2 5 1

55. Averages from Frequency Tables
The frequency table shows the weights of eggs bought in a shop
weight
58g
59g
60g
61g
62g
63g
frequency 3 7 11 9 8 2
Mode = most common weight = 60g
Position of median =
= 20.5 , so the median = 60g
Mean =
= 60.45g

56. Sam and his partner recorded the number of times they could hit a ping pong ball between them without it going off the table. Their results are in the table below.
Consecutive hits (h)
Frequency
Midpoint
Midpoint x Frequency
0 < h ≤ 20 3
20 < h ≤ 40 17
40 < h ≤ 60 25
60 < h ≤ 80 56
80 < h ≤ 100 8
100 < h ≤ 120
Total
What is different about this table?
What difference does this make to what you know or do not know about the data?
What can you say about the mode, mean, median or range?

57. The amounts spent by 50 customers at a shop are shown in the table.
HOMEWORK
The amounts spent by 50 customers at a shop are shown in the table.
(a) Work out the probability that a customer chosen at random spent more than £20.
(b) Explain why it is not possible to work out the probability that a customer chosen at random spent exactly £8.
(c) Use midpoints to calculate an estimate of the mean amount spent at the shop.
(a) 19/50 or 0.38 or 38%, (b) the original data is not known, or we do not know if any of the 18 spent exactly £8, (c) £16.60 (not £16.6)

58. Company A Salary (£) Frequency 0 < £ ≤ 10 000 2
0 < £ ≤ 2
< £ ≤ 10
< £ ≤ 19
< £ ≤ 16
< £ ≤ 3

59. Company B Salary (£) Frequency 10 000 < £ ≤ 20 000 6
< £ ≤ 6
< £ ≤ 17
< £ ≤ 27
Which company will you choose to work for?
Give reasons for your answer.
You must show your working.

60. Comparing two sets of data
Two classes, A and B, did the same test. For class A the mean score was 31 and the range was 28. Here are the scores for class B:
Scores
Frequency
0 < s < 10 2
10 < s < 20 4
20 < s < 30 9
30 < s < 40 12
40 < s < 50 3
Clues: modal class & class containing the median score – any use?
estimate of mean? can you find the range?

61. A Mean Set
A set of five numbers has: A mode of 12 A median of 11 A mean of 10 What could the numbers be?

62. Find the 5 numbers from the following list that have:
a mode of 15
a median of 14
a mean of 12
a range of 10