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Grade 9

Maths

Basic information

Class 4 21 April 2020 Collecting and organising data

Class 5 22 April 2020 - Represent data

Class 6 23 April 2020 - Data handling

Class 7 24 April 2020 - Data handling

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GRADE 9 GREY COLLEGE MATHS

Background information of data handling

COLLECT, ORGANISE AND OBTAIN SUMMARY STATISTICS

Collecting data

Data The results of a statistical investigation are called data. For example, the set of marks obtained by a Grade 9 class for a class test given is called data. Raw data is data that is not organised in any meaningful way. This data must be organised and presented in different ways so that it can be interpreted and analysed.

Discrete data: This is data that is counted. The data values are whole numbers. For example, the number of spectators attending the different matches during the 2014 FIFA World Cup is discrete data

Continuous data:

This is data that is measured. The data values are rational numbers. For example, measuring the heights of the soccer players in the World Cup is continuous data since the heights are not restricted to whole numbers. The heights can be 1,85 m or 1,76 m.

Survey A survey is used to collect data from a selection of people in a community. If data is to be collected from all people in that community, then a census is taking place

Questionnaire: A questionnaire is used to collect data when doing a survey

Population A population is made up of the entire group of people studied. For example, a population could be all women in South Africa. Another population could be all the members of a particular religion.

Sample A sample of a population is a small selection from the population. It must be representative, random and unbiased and must represent all people in the larger population. People must be selected at random so as to avoid bias leading to misleading results.

Biased samples

A sampling method is biased if it tends to give samples in which some characteristic of the population is under-represented or over-represented. Biased samples are not representative of the whole population, and so could lead to misleading results.

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Random samples

A random sample has two properties:

• It is unbiased. This means that each item in a population had the same chance of being chosen.

• It is independent. This means that the selection of one item had no influence on the selection of the other items.

Data handling Data handling involves the following:

• Collecting data

• Sorting the data

• Representing the data graphically

• Interpreting results

• Making conclusions

Display of discrete data

Bar graph A bar graph is a diagram consisting of a series of parallel bars (either horizontal or vertical). The lengths of the bars show frequency, making the bars easy to compare. Example 1 80 households were surveyed and the number of children in each family was recorded as follows:

0 1 3 3 4 2 3 2 1 5 2 0 3 1 2 5 3 4 1 3 3 1 0 2 3 1 2 4 5 2 1 5 2 4 1 3 2 0 3 5 2 1 0 3 2 2 5 5 1 2 3 2 0 4 1 4 3 2 5 4 1 4 2 1 3 5 0 5 1 2 4 2 4 3 2 3 3 0 2 5

Number of children in the family

Tally Frequency

0 1 2 3 4 5

|||| ||| |||| |||| ||||

|||| |||| |||| |||| |||| |||| |||| ||

|||| |||| |||| |||| |

8 14 20 17 10 11

80

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Draw a vertical bar graph to illustrate this information.

Compound bar graphs

a) Dual bar graph: Dual bar graphs are used when two different sets of info are given on connected topics.

Example 20 people recounted which TV station they were watching at 8:15 pm on two consecutive nights in July 2005. The results were:

Station 1e night 2e night

TV1 TV2 TV3

Mnet e-TV

6 4 6 3 1

7 1 6 4 2

20 20

A dual bar chart representing the number of people watching various TV stations at 8:15 pm on two consecutive nights in July 2005:

0

5

10

15

20

0 1 2 3 4 5

Frequency

Number of children per family

0

1

2

3

4

5

6

7

TV1 TV2 TV3 Mnet e-TV

Frequency 1e aand

2e aand

1st night

2nd night

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Pie Chart A pie chart is used for displaying information. Example

1. 70% of the earth surface is water. The rest is land, 11% of the earth is habitable, 6% is too cold, 4% is too mountainous and 9% is too dry.

A revolution is 360o.

% Calculation to nearest whole no

H2O 70 70% 360 252o o = 252o

Land – habitable 11 11% 360o =39,6o 40o

Land – too cold 6 6% 360o =21,6o 22o

Land – too mountainous

4 4% 360o =14,4o 14o

Land – too dry 9 9% 360o =32,4o 32o

Total 100 360o

Water

bewoon

koud

bergagtig

droog

Habitable

Cold

Mountainous

Dry

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Broken line graph

Can help you to: - See patterns or trends - Spot relationships between data Graph showing Norma’s temperature

03:00 - temp = 38,4oC 06:00 - temp = 38,2oC Temp dropped at a constant rate between 03:00 - 06:00. But at 04:00 her temp had risen to 38,9 oC and by 06:00 dropped to 38,2 oC.

Stem and leave diagrams Data:

145; 147; 171; 172; 171; 159; 154; 157; 161; 162; 163; 162; 164; 164; 166

Draw a tally frequency table for the above data:

Mandi

Tally table showing heights in cm. 140 – 149 ||

150 – 159 ||| 160 – 169 |||| ||

170 – 179 |||

180 – 189

37

37.5

38

38.5

39

39.5

40

00:00 03:00 06:00 09:00 12:00 15:00 18:00

Temperatuur

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Draw a stem and leaf diagram for the above data:

Heights of girls in cm

Stem Leaves 14 5 7

15 4 7 9 16 1 2 2 3 4 4 6

17 1 1 2

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Key: 14

5 represents 145cm

Jane orders her stem and leaf diagram and adds a key to explain it.

Scatterplot

A scatter plot gives a visual representation of the relationship between 2 variables on a Cartesian plane. Outliers are data values that are numerically far removed from the rest of the data values.

The line is called the trend line and shows the general trend of the relationship. Example The scatter plot represents the relationship between English marks and Maths marks. The point (10;90) represents a learner who obtained 10% in Maths, but 90% in English. There is 2 outliers, A and B

A

B

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Grouping data Ruth manages a supermarket. As part of her investigation she records how many items each customer standing in the queue buys. Ruth wanted to know how to organise the tills in her supermarket. She then drew a histogram to illustrate the information: Here are her results:

24 9 4

27 10 5

2 5

18

4 17 1

7 25 3

13 5

21

24 18 24

7 10 18

22 6

20

25 27 3

32 11 8

26 30 9

8 33 26

3 2

34

10 16 25

12 29 1

29 4 5

3 29 25

6 25 19

14 2

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Group this data and choose intervals or classes of 1 – 5; 6 – 10; 11 – 15; 16 – 20 etc. Solution:

Number of Items Tallies Number of items bought

1 – 5 6 – 10

11 – 15 16 – 20 21 – 25 26 – 30 31 – 35

|||| |||| |||| | |||| |||| |

|||| |||| |||

|||| |||| |||| ||||

|||

16 11 4 8 9 9 3

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Histograms

A bar graph is used to display discrete data. A histogram is used to display grouped data. The horizontal axis shows class intervals, and there are no graphs between the bars.

Histogram (Spreadsheet1 10v*63c)

0 5 10 15 20 25 30 35 40

Aaantal items gekoop

0

2

4

6

8

10

12

14

16

18

No

of

ob

s

• No gaps between bars of the histogram.

• The horizontal scale follows on from one bar to the next

• The vertical scale measures the frequency.

Frequency polygon

A frequency polygon is a line-based graphical representation of the frequency of an event occurring in a data set.

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Measure of central tendency

Three measures of central tendency or averages are:

a) the mean= sum of scores

no of scores

b) the mode = the number which appears most c) the median = middle most value Example Scores: 3, 9, 11, 28, 37, 20 Mean

3 9 11 28 37 20

6

108

6

18

+ + + + +=

=

=

Mode: 3, 9, 11, 20, 28, 37 No mode, all numbers appear only once.

Median = 11 20

2

+

= 15,5 Example Work out the mode, median and mean of the set of data:

Value 3 4 5 6

Frequency 1 4 3 2 The table tells us that 3 occurred once, that 4 occurred four times, that 5 occurred three times and that 6 occurred twice.

• The mode is the number with the greatest frequency. There are more 4’s than any other number. The mode is 4.

• To find out how many numbers there are we add up the frequency (n = 10) There are 10 numbers. The median lies between the 5th and 6th numbers when they are written in order: 3 4 4 4 4 | 5 5 5 6 6

Median = 4+5

2= 4,5

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• The mean= sum of scores

no of scores

The total value of the numbers = (1×3 ) + (4 × 4) + (3 × 5) + (2 × 6) = 46 n =10

The mean= 46

10= 4,6.

Example Given: 33 57 46 69 28 68 32 60 65 54 54 40 46 45 26

• Mode = 46 and 54. It is called bimodal.

• Median = 46.

• Mean = 26+28+32+33+40+45+46+46+54+54+57+60+65+68+69

15= 48,2

Stem leaves

2 3 4 5 6

6,8 2,3

0,5,6,6 4,4,7

0,5,8,9

Measures of dispersion Range is a simple measure of spread. Range = Largest value – smallest value Range cannot be used with group data.

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GRADE 9 GREY COLLEGE 2020

MATHS Class 4 21 APRIL 2020

Do the following in Book 2 (or on paper) EXERCISE 1

1.

2.

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GRADE 9 GREY COLLEGE 2020

MATHS Class 5 22 APRIL 2020

Do the following in Book 2 (or on paper) EXERCISE 2

1.

2.

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3.

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GRADE 9 GREY COLLEGE 2020

MATHS Class 6 23 APRIL 2020

Do the following on the document (When school reopen, hand-in to teacher)

EXERCISE 3 PART 1

1. The average amount that learners spend at the Tuckshop (in Rand), are given below:

30 51 42 51 63 45 65 55 48 68 77 32 53 82 42 52 37 57 67 59 41 40 56 36 55 88 48 60 47 81

1.1. Draw the table below in your answer book and complete the frequency table.

Amount spend in Rand Frequency

30-39

40-49

50-59

60-69

70-79

80-89

1.2. Represent the data on a Histogram.

1.3. Draw a frequency polygon. Use the diagram you have drawn in question 1.2.

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2. 108 Learners are asked to tell us what their favourite thing for breakfast is. In the circle

diagram below you will find the results to their answers. Use the circle diagram to answer

the questions that follow:

2.1. How many learners like to have cereal for breakfast?

2.2. How many learners did not vote for pancakes?

2.3. What percentage of the learners likes to have a Hash brown for breakfast?

2.4. How many degrees in this circle diagram is used for the toast segment?

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3. A class of 48 learners at Menlopark High School were asked to indicate their favourite

colour. The results were as follows: Red – R, Green – G, White – W, Blue – B, Orange - O.

3.1 Complete the following table:

3.2 Draw a Pie chart to represent the information graphically

B W B B R R G B R O R B

R B R B B O B B G B B B

B B O B G B B R B B W R

G R B B W R R G B R B G

Colour Tally Frequency Fraction

R

G

W

B

O

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GRADE 9 GREY COLLEGE 2020

MATHS Class 7 24 APRIL 2020

Do the following on the document (When school reopen, hand-in to teacher)

EXERCISE 3 PART 2

4.

4.1 On which day were the two plants equal in height?

4.2 On which day did plant B show no grow?

4.3 How much taller is plant A than plant B on day 8?

4.4 How much smaller is plant B than plant A on day 7?

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5. Consider the graph below:

5.1 What does the data graph represent?

5.2 Determine the mean number of cubs born per year.

5.3 Can you give possible reasons for the outliers?

5.4 Remove the outliers. What effect does this have on the mean number of cubs born per year.

5.5 Write a few sentences on your findings. Include a prediction for 2004. 6. Find a snip let out of a newspaper or magazine of a graph that represents any data.

Paste it in your project. Then, in your own words, describe in a short paragraph which data is represented by the graph.