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Module 1 Higher GCSE Mathematics Revision

Advice

- Do not spend too long on 1 question If you

cannot see what to do leave it out return to it

at the end if you have time. - Show working whenever you can You may get

method marks even if your final answer is wrong. - Remember to look at the formula page There may

be something there that could help you. - Dont panic! You can do this!!!

Cumulative frequency

A golf club has 200 members. Their ages are shown

in the frequency table below.

A cumulative frequency (or a less than) table

can be drawn from this data.

8

8

26

34

32

66

45

111

37

148

29

177

16

193

7

200

How old is the youngest/oldest person?

We can now use this to draw a cumulative

frequency graph.

8

8

10

34

20

34

66

30

66

111

40

111

50

148

148

60

177

177

70

193

193

80

200

200

We can now use this to draw a cumulative

frequency graph.

8

34

66

111

148

177

193

200

Cumulative Frequency graph.

We can now use this to find the following

information..

Median

37

Lower quartile

25

Upper quartile

51

Lowest Value

0

Highest Value

80

Interquartile range

51 - 25

26

This information can now be used to draw a box

and whisker diagram..

Averages

Connect these together

Mean

Most common

Add them together and divide by how many there are

Median

Mode

Put in order then find the middle

Difference between biggest and smallest

Range

Which is the odd one out?

Averages

Find the mean, median, mode and range of these

values.

2

8

7

4

5

6

9

7

Mean (2 8 7 4 5 6 9 7) 8

48 8

6

Median

6.5

Mode

7

Range

7

9 - 2

Moving Averages

Why use them?

- Moving Averages, when graphed, allow us to see

any trends in data that are cyclical - By calculating the average of 2 or more items in

the data, any peaks and troughs are smoothed out.

265

269.25

265.25

270.75

4 Point Moving Average

4 period Moving Average

500

x

400

x

x

300

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

200

x

x

x

100

1

2

3

4

1

2

3

4

1

2

3

4

1998

1996

1997

Mean from frequency table

ABC Motoring

- Here are the number of tests taken before

successfully passing a driving test by 40

students of ABC Motoring

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.

We can group the results into a frequency table.

ABC Motoring

- Thats better!

Finding the Mean

Remember, when finding the mean of a set of data,

we add together all the pieces of data.

This tells us that there were nine 1s in our

list. So we would do 111111111 9

It is simpler to use 1x9!!

We can do this for every row.

Finding the Mean

107

40

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.

We now need to add these together

107

40

The Mean is

107 40 2.7 (1dp)

ABC Motoring

- Students who learn to drive with ABC motoring,

pass their driving test after a mean number of

2.7 tests.

Mean from Grouped frequency table

Grouped data

Here are the Year Ten boys javelin scores.

How could you calculate the mean from this data?

How is the data different from the previous

examples you have calculated with?

Because the data is grouped, we do not know

individual scores. It is not possible to add up

the scores.

Midpoints

It is possible to find an estimate for the

mean. This is done by finding the midpoint of

each group. To find the midpoint of the group

10 d lt 15 10 15 25 25 2

12.5 m

Find the midpoints of the other groups.

Estimating the mean from grouped data

1 7.5

7.5

7.5

8 12.5

100

12.5

12 17.5

210

17.5

10 22.5

225

22.5

3 27.5

82.5

27.5

1 32.5

32.5

32.5

1 37.5

37.5

37.5

36

695

TOTAL

Estimated mean 695 36

19.3 m (to 1 d.p.)

1 Find the modal group, median and estimate the

mean from the table below.

- Michelle keeps a record of the number of minutes

her train is late each day. The table shows her

results for a period of 50 days.

Probability

Three boys ring Jane and ask her for a date

Probability tree diagrams

- The probability that it will rain on Monday is

0.2. The Probability it will rain on Tuesday is

0.3. - What is the probability that it will rain on

Monday and Tuesday?

Tuesday

It rains

0.3

Monday

- We can solve this problem by drawing a tree

diagram.

We know that the probability is 0.2

It rains

0.2

There are two possible events here It rains or

It does not rain

0.7

It does not rain

Now lets look at Tuesday

The probability that it rains on Tuesday was

given to us as 0.3. We can work out that the

probability of it not raining has to be 0.7,

because they have to add up to 1.

It rains

0.3

0.8

It does not rain

What is the probability?

Well, raining and not raining are Mutually

Exclusive Events. So their probabilities have to

add up to 1.

1 0.2 0.8

We now have the required Tree Diagram.

0.7

It does not rain

We wanted to know the probability that it rained

on Monday and Tuesday.

0.2 x 0.3 0.06

We can work out the probability of both events

happening by multiplying the individual

probabilities together

This is the only path through the tree which

gives us rain on both days

So the probability that it rains on Monday and

Tuesday is 0.06

Actually, we can work out the probabilities of

all the possible events

0.2 x 0.7 0.14

The probability of rain on Monday, but no rain on

Tuesday is 0.14

0.8 x 0.3 0.24

The probability that it will not rain on Monday,

but will rain on Tuesday is 0.24

0.8 x 0.7 0.56

The probability that it does not rain on both

days is 0.56

Lets look at the completed tree diagram

The end probabilities add up to 1. Remember this!

It can help you check your answer!

What do you notice?

Stem and Leaf Diagrams

- Numerical bar charts

Stem and Leaf Diagrams

Here is a set of data 14, 28, 17, 21, 23, 23,

19, 16, 26, 24, 24, 13, 20, 16, 18, 15, 22, 29,

21, 25 Decide on suitable groups tens are too

big, fives would give four groups - ok

4

2

5

1

9

5

8

6

0

3

4

4

6

6

9

3

3

1

7

8

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

2

2

10 to 14

1 1 2 2

15 to 19

20 to 24

25 to 29

Stem and Leaf Diagrams

Now we need to put the leaves in numerical order

1 3 4 1 5 6 6 7 8 9 2 0 1 1 2

3 3 4 4 2 5 6 8 9

Interpreting Stem and Leaf Diagrams

1 3 4 1 5 6 6 7 8 9 2 0 1 1 2

3 3 4 4 2 5 6 8 9

Mode most common 16, 21, 23 and 24 (all

happen twice) Median middle one (they are

already in order) 20 pieces of data looking

for 10th and 11th both are 21 Range biggest

smallest 29 13 16 Dont usually get asked

for the mean.

Your Turn

- Draw a stem and leaf diagram of this data
- 2.3, 3.6, 4.5, 3.1, 5.8, 6.2, 4.2, 5.0, 3.1, 3.7,

2.2, 2.8, 5.1, 6.0, 3.0, 4.9, 4.4, 5.3 - From the diagram, find the mode, median and range

Good Luck!!!