25-Aug-14Created by Mr. Lafferty1 Statistics Mean Mean from a Frequency Table Range of a Set of Data...

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty 11

StatisticsStatistics

Mean

Mean from a Frequency Table

Range of a Set of Data

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Median and Mode

Grouped Frequency Table

Level F

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty 22ww

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Level F

Starter

Q1. Round to 2 decimal places

Q2. Add 2.34 + 5.03 + 7.2

Q3. Solve for x

(a) 52.567 (b) 62.155

2 20 8x x


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Level E

Aims of the lesson

1. Explain the meaning of the keyword Mean

2. Calculate the mean for given data.

11 Apr 2023 Created by Mr. Lafferty 4

The meanThe mean is the most commonly used average.

To calculate the mean of a set of values we add together the values and divide by the total number of values.

For example, the mean of 3, 6, 7, 9 and 9 is

3 + 6 + 7 + 9 + 95

345

6.8

Mean =Sum of values

Number of values


Two dice were thrown 10 times and their scores were added together and recorded. Find the mean for this data.

7, 5, 2, 7, 6, 12, 10, 4, 8, 9

Mean

7 + 5 + 2 + 7 + 6 + 12 + 10 + 4 + 8 + 910

7010

7


Now try Exercise 4 Ch5 (page 106)

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Level F

Average / MeanAverage / Mean


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Level F

Lesson Starter

Q1. 75% of £200

Q2. How long between 8:40am to 1.20pm

Q3. 36.9 x 6

Q4. 34.7 x 20

Q5. Find the mean for the set of numbers

-7, 10, 6, 3


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Level F

Aims of the Lesson

Find the mean for a set of data without a calculator

using the mean difference


Two dice were thrown 10 times and their scores were added together and recorded. Find the mean for this data.

7, 5, 2, 4, 6, 12

Scores 7 5 2 4 6 12

Assumed mean 5

2 0 -3 -1 1 7

Mean difference

2 + 0 + (-3) + (-1) + 1 + 76

= 1

Mean =

5 +1 = 6


Find the mean for this data without a calculator.

112, 118, 121, 124, 129

Scores 112 118 121 124 129

Assumed mean 120

-8 -2 1 4 9

Mean difference

(-8) + (-2) + 1 + 4 + 95

= 0.8

Mean =

120 +0.8 = 120.8


Now try Exercise 4.2 Ch5 (page 109)

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Level F

Average / MeanAverage / Mean

11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Starter QuestionsStarter Questionsw

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2. Simplif y the ratio 6:28

1. Mutliply out 2y( y - 4)

3. 10% of £22

4. Tidy up the expression

7 - (- 10) x 3

Level F

11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

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1.1. Add a third column to a Add a third column to a frequency table.frequency table.

1. To explain how to work out the mean by adding in a third column to a Frequency Table.

Frequency Frequency TablesTables

Working Out the Mean

2.2. Work out the mean from a Work out the mean from a frequency Table.frequency Table.

Level F


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No ofNo of

Coins Coins ((cc))

Freq.Freq.

(f)(f)

Example : This table shows the numberof coins in the pockets of some children.

5

1

2

16

3

5

1

2

3

4

5

Totals



Adding a third column to this tablewill help us find the total number ofcoins and the ‘Mean’.

5 x 1 =5

1 x 3 = 3

2 x 5 = 10

3 x 4 = 12

5 x 2 = 10

40

Mean Number of coins = 40=2.5 coins

16

f x Cf x C

Level F


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No of No of SiblingSiblings (s (SS))

Freq.Freq.

(f)(f)

Example : This table shows the numberof brothers and sisters of pupils in an S2 class.

9

6

1

30

1

13

0

1

2

3

5

Totals



Adding a third column to this tablewill help us find the total number ofsiblings and the ‘Mean’.

0 x 9 =0

2 x 6 = 12

5 x 1 = 5

3 x 1 = 3

1 x 13 = 13

33

Mean Number of siblings

33= =1.1 siblings

30

S x S x ff

Level F


Now try Exercise 5.1

Ch5 (page 111)

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Level E

Lesson Starter

Q1. 70% of £500

Q2. How long between 8:12am to 2.09pm

Q3. 75.9 x 7

Q4.

Q5. The answer to a question is 81. Writedown the question.

1200 1300

Find arrow value


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2.2. Work out values of Mean, Work out values of Mean, Median, Mode and Range.Median, Mode and Range.

1. To define the terms Mean Median, Mode and Range for a set of data.

1.1. Know the terms Mean, Know the terms Mean, Median, Mode and Range.Median, Mode and Range.

Different AveragesLevel F


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1+1+1+1+2+3+26The Mean = =5

7

Find the mean of the set of data 1, 1, 1, 1, 2, 3, 36

Sum of all the numbersThe Mean =

No. of Number

Can you see that this is not the most suitable of averages sincefive out of the six numbers are all below the mean of 5



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“measure of central tendency” but should also indicate

what the distribution of data looks like.

This is why we have 3 different types of averages to consider

1. The Mean

2. The Median (put the data in order then find the MIDDLE value)

3. The Mode (the number that appears the most)

For the above data the Median or Mode is a better average = 1

Different Averages


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Different Averages

Example :

Find the median and mode for the set of data.

10, 2, 14, 1, 14, 7

Median=1,2, ,17,10 4,14 Mode =14

7 +10 17=Median= =8.5

2 2

Level F



Ch5 (page 115)

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Level F

Lesson Starter

Q1. 20% of £800

Q2. 12000 divided by 60

Q3. Tidy up the following 2x + 5y – 3x – 6y

Q4.

Q5. The answer to a question is 60. Writedown the question.

A circle is divided into 10 equal pieces.The whole circle represents 100%. What value is one piece.


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Level F

Aims of the lesson

1. Explain the meaning of the keyword Range

2. Calculate the mean and range for given data.


Finding the rangeThe range of a set of data is a measure of how the data is spread across the distribution.

To find the range we subtract the lowest value in the set from the highest value.

Range = highest value – lowest value

When the range is large; the values vary widely in size.

When the range is small; the values are similar in size.


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Level F

The Range

Example : find the range for the following

(a) 3, 1, 4, 10

(b) -3, 8, -6, 1, 7, 5

(c) The highest and lowest every recorded temperature for Glasgow are 35.3oC and -15.5oC respectively.

Find the value of the range.

10 – 1 = 9

7 – (-6) = 13

35.3 – (-15.5)

= 50.8oC


Now try Ex7.1 & 7.2

Ch5 (page 117)

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StatisticsStatistics Working Out StatisticsLevel F


Starter QuestionsStarter Questionsw

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2. Calculate (a) (-3m) x (-4m) (b) (2b) x (3a)

1. Find the perimeter and area of the shape.

3. Find the mean of the data set

3,5,5,7,10

6h

2a

Level F


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1.1. Construct Grouped Construct Grouped Frequency TableFrequency Table

1. To explain how to construct and interpret Grouped Frequency Tables.

Frequency Tables

2.2. Interpret Table.Interpret Table.

Grouped Frequency Grouped Frequency TablesTables

Level F


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When a set of data is large, the numbers have to begrouped into “class intervals”.• Each interval must have the same number of values

• Ideally, there should be between 6 to 10 intervals

Frequency Tables

We will now construct a Frequency Table


Level F


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Frequency Tables

Class Class IntervalsIntervals

TallyTally FrequencFrequencyy

12 23 41 55 7715 32 40 51 6921 12 16 43 5671 32 75 34 4255 76 21 73 2256 41 19 20 4778 17

Example : The test scores for a classare given below. Construct a FrequencyTable for the results.

1

6

3

5

6

6

5

10-19

20-29

30-39

40-49

50-59

60-69

70-79

Choose suitable

Class interval

Level FWhat is the modal class

interval10 – 19, 40 –

49 and 70 - 79



Ch5 (page 120)

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StatisticsStatistics Working Out StatisticsLevel F

25-Aug-14Created by Mr. Lafferty1 Statistics Mean Mean from a Frequency Table Range of a Set of Data...

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