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# 11 Math A - Data (Types, Collecting, Preparation & Display) - tyoun158

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Tweet## Triston Young

on 7 March 2011#### Transcript of 11 Math A - Data (Types, Collecting, Preparation & Display) - tyoun158

Collection & Recording DATA Types of Data Catagorical Data Data which can be placed into categories Hair Colour

Favorite Food

Mode of transport to school

Also when there is a scale of responses to choose from Brown, Black, Blonde, Red etc.

Sushi, Steak, Seafood etc.

Car, Bike, Bus etc.

Strongly disagree to strongly agree or never to always Categorical - Nominal Data Categorical - Ordinal Data No set of desired responses, just a collection of responses Recorded data would have a set order of responses

i.e. tick the appropriate box or circle etc. Numerical Data Data which involves amounts, counting, numbers, measurements etc. Number of cars per household

Number of siblings

Scores on a test

Peoples heights

Daily temperatures 0,1,2,3, etc.

0,1,2,3, etc.

23,36,32,30, etc.

162.2cm,185.8cm,145.5cm, etc.

22 C, 28 C, 32 C, etc. o o o Numerical - Discrete Data Numerical - Continuous Data Usually whole numbers of things

i.e. can't have half a sibling or car Are the results of taking measurements

i.e. Heights, temperatures, lengths etc. N.B. Marks on a test and shoe sizes are also types of discrete data even though they can have half marks and half sizes N.B. Continuous data is said to allow for more accuracy and hence can have more precise measurements. i.e. someones height can be 162.2358cm Types of Questioning Open Questions: No predetermined desired response Closed Questions: Making some choose from a desired set of responses i.e. yes/no responses What did you do on the weekend?

Where would you like to go tomorrow? Did you go to the beach on the weekend?

Which do you prefer Tap or Bottled water? What type of Data are these 1. The number of races each house won at the swimming carnival 2. The amount of water used in households 3. The television program people watch at 7:00pm Recording of Data The favorite sports of Yr. 10 students.

a) How many students?

b) What's the most popular sport?

c) What's the least popular sport/s?

Tally: A running scorecard

Frequency: The number of times the option was chosen Displaying of Data Data is often initially

placed into a table with: Column Graphs In a column graph the Categories are along the horizontal and the Frequency is along the vertical axis. Categories Frequency Note: there is a gap between columns and they are between the marks Sector Graphs Will require the use of a

calculator and a protractor Create an extra column in your table to calculate the size of the sector Calculate each angle as a fraction of 360 o _______ Frequency

Total number of results x 360 = Angle _______ _______ ___________________ _______ Angle _______ _______ _______ _______ _______ _______ _______ _______ __ __ Total 24 o Eg. AFL Angle = 6

24 __ x 360 = 90 o o 90 o 45 30 30 15 15 30 o o o o o o o 105 Histograms Important Features: There is a half gap at the start and end of the graph

Horizontal axis has the scores or categories

Vertical axis has the frequency

The columns are set in the centre of the marks

No gaps between the columns Frequency Polygon Important Features: Starts at the origin of the graph (0,0)

Joins the centre of the tops of the columns

Ends half a gap after the last column Important Notes When your categories come in a range i.e. 0-9, 10-19 etc. You need to give the centre of the range for the marker on the Histogram on the horizontal axis 5 Number Summary Lowest Value (L): Lower Quartile Value (Q ): Median (M): Upper Quartile Value (Q ): Highest Value (H): Lowest value in the data set The median of the Lower half of values The middle score The median of the Upper half of values Highest value in the data set Stem-and-Leaf Plots Stem | Leaf Leaf has only one digit of the number

Stem has the other digits

No commas in the Leaf

A Key gives a way to read the plot 100,101,125,136,133,129 Stem | Leaf | | | | 10 0 1 12 5 9 13 3 6 Key 10|0 = 100 There is a special case Stem-and-Leaf example 10,11,12,12,10,11,12,12,13,14,14,15,18,19,20,22,29,33,34,34,35,36,39 Stem | Leaf | | | | 1 0 0 1 1 2 2 2 2 3 4 4

1* 5 8 9

2 0 2 9

3 3 4 4 5 6 9 When there are too many values you can break a Stem in half using the * symbol Key 1|0 = 10

1*|5 = 15 1|something = is for the numbers from 10-14

1*|something = is for the numbers from 15-19 Box-and-Whisker Plots ___________________ | | | | | | | | | | | | | 10 12 14 16 18 20 22 24 26 28 30 32 34 | | _________ _________ | | ________ | | ________ | | Lowest Lower Quartile Upper Quartile Median Highest 5 Number Summary from a

Box-and-Whisker Plot Lowest = ?

Lower Quartile Value = ?

Median = ?

Upper Quartile Value = ?

Highest = ? Statistical Measures

Mean:

Median:

Mode: the average the middle score the most common score Calculating the Mean = Finding the Median = Sum of the scores

Number of scores _______________ Number of scores +1

2 _______________ Finding Median of odd number of scores If there are 3,5,7,9,11 etc. scores number of scores +1

2 Median = _______________ = 11+1

2 ___ = 6th score is the median Finding Median of even number of scores If there are 2,4,6,8,10 etc. scores Median = _______________ number of scores +1

2 = _____ 10+1

2 = the average of the 5th and 6th scores 5.5 6 Median = 5th score + 6th score

2 ____________ Questions: Exercise 9F - Stem-and-leaf plots

Questions: Odd Questions Only

1,3,5,7,9,11 1 3 Interquartile Range (IQR): Upper Quartile value - Lower Quartile value

Q - Q 1 3 Find the 5 Number Summary of the

following data sets: Question 1: Example: Question 2: Question 3: 33, 33, 36, 39, 40, 42, 43, 45, 46, 47, 50 1.2, 1.3, 1.5, 1.6, 1.6, 1.6, 1.8, 1.9, 2.0, 2.1, 2.2, 2.2, 2.3, 2.3, 2.5, 2.9, 3.0, 3.3, 3.7, 4.2 29, 33, 46, 49, 60, 62, 63, 95, 116, 147, 150 52.5, 56, 57.5, 58, 58.5, 58.5, 60.5, 61, 63,

78.5, 81, 83.5, 88, 88.5, 89.5, 90, 92.5, 93, 99 Highest:

Lowest: Highest:

Lowest: Highest:

Lowest: Highest:

Lowest: Median: Median: Median: Median: Upper Quartile (Q ):

Lower Quartile (Q ): Upper Quartile (Q ):

Lower Quartile (Q ): Upper Quartile (Q ):

Lower Quartile (Q ): Upper Quartile (Q ):

Lower Quartile (Q ): 1 1 1 1 3 3 3 3 Exercise 9G Questions 1-10 Chapter 9 Review Even Questions:

2,4,6,8,10,12 Misrepresentation of Data: To determine whether graphical data has been misrepresented, check: scale on both axes is linear

scales on vertical and horzontal axes have not been lengthened or shortened to give a biased impression

certain values have not been omitted in the graph

picture graphs are drawn to represent a height not a volume (goes up or down in equal amounts) (no missing values on the axes) (it is not a just part of the whole graph or has missing values) (the size of the picture is not proportional to it's reading on the

vertical axis) Changes of Scale Given Data of: By changing the vertical axis we can make the increase over the Year seem like a larger growth than it actually was. Omitting Values By omitting the values for April-June (A-J) it seems like the increase has been constant over the entire year Omitted A-J Value Another Example Which one would you use to support the notion that we are wasting tax payers money on police strength? Why? Showing a quicker increase (greater slope) Non-Linear Scale (different sized gaps) This graph has

even sized gaps Pictorial Representation The picture shows a larger growth than that of the vertical axis Exercise 9D

Even Questions

Full transcriptFavorite Food

Mode of transport to school

Also when there is a scale of responses to choose from Brown, Black, Blonde, Red etc.

Sushi, Steak, Seafood etc.

Car, Bike, Bus etc.

Strongly disagree to strongly agree or never to always Categorical - Nominal Data Categorical - Ordinal Data No set of desired responses, just a collection of responses Recorded data would have a set order of responses

i.e. tick the appropriate box or circle etc. Numerical Data Data which involves amounts, counting, numbers, measurements etc. Number of cars per household

Number of siblings

Scores on a test

Peoples heights

Daily temperatures 0,1,2,3, etc.

0,1,2,3, etc.

23,36,32,30, etc.

162.2cm,185.8cm,145.5cm, etc.

22 C, 28 C, 32 C, etc. o o o Numerical - Discrete Data Numerical - Continuous Data Usually whole numbers of things

i.e. can't have half a sibling or car Are the results of taking measurements

i.e. Heights, temperatures, lengths etc. N.B. Marks on a test and shoe sizes are also types of discrete data even though they can have half marks and half sizes N.B. Continuous data is said to allow for more accuracy and hence can have more precise measurements. i.e. someones height can be 162.2358cm Types of Questioning Open Questions: No predetermined desired response Closed Questions: Making some choose from a desired set of responses i.e. yes/no responses What did you do on the weekend?

Where would you like to go tomorrow? Did you go to the beach on the weekend?

Which do you prefer Tap or Bottled water? What type of Data are these 1. The number of races each house won at the swimming carnival 2. The amount of water used in households 3. The television program people watch at 7:00pm Recording of Data The favorite sports of Yr. 10 students.

a) How many students?

b) What's the most popular sport?

c) What's the least popular sport/s?

Tally: A running scorecard

Frequency: The number of times the option was chosen Displaying of Data Data is often initially

placed into a table with: Column Graphs In a column graph the Categories are along the horizontal and the Frequency is along the vertical axis. Categories Frequency Note: there is a gap between columns and they are between the marks Sector Graphs Will require the use of a

calculator and a protractor Create an extra column in your table to calculate the size of the sector Calculate each angle as a fraction of 360 o _______ Frequency

Total number of results x 360 = Angle _______ _______ ___________________ _______ Angle _______ _______ _______ _______ _______ _______ _______ _______ __ __ Total 24 o Eg. AFL Angle = 6

24 __ x 360 = 90 o o 90 o 45 30 30 15 15 30 o o o o o o o 105 Histograms Important Features: There is a half gap at the start and end of the graph

Horizontal axis has the scores or categories

Vertical axis has the frequency

The columns are set in the centre of the marks

No gaps between the columns Frequency Polygon Important Features: Starts at the origin of the graph (0,0)

Joins the centre of the tops of the columns

Ends half a gap after the last column Important Notes When your categories come in a range i.e. 0-9, 10-19 etc. You need to give the centre of the range for the marker on the Histogram on the horizontal axis 5 Number Summary Lowest Value (L): Lower Quartile Value (Q ): Median (M): Upper Quartile Value (Q ): Highest Value (H): Lowest value in the data set The median of the Lower half of values The middle score The median of the Upper half of values Highest value in the data set Stem-and-Leaf Plots Stem | Leaf Leaf has only one digit of the number

Stem has the other digits

No commas in the Leaf

A Key gives a way to read the plot 100,101,125,136,133,129 Stem | Leaf | | | | 10 0 1 12 5 9 13 3 6 Key 10|0 = 100 There is a special case Stem-and-Leaf example 10,11,12,12,10,11,12,12,13,14,14,15,18,19,20,22,29,33,34,34,35,36,39 Stem | Leaf | | | | 1 0 0 1 1 2 2 2 2 3 4 4

1* 5 8 9

2 0 2 9

3 3 4 4 5 6 9 When there are too many values you can break a Stem in half using the * symbol Key 1|0 = 10

1*|5 = 15 1|something = is for the numbers from 10-14

1*|something = is for the numbers from 15-19 Box-and-Whisker Plots ___________________ | | | | | | | | | | | | | 10 12 14 16 18 20 22 24 26 28 30 32 34 | | _________ _________ | | ________ | | ________ | | Lowest Lower Quartile Upper Quartile Median Highest 5 Number Summary from a

Box-and-Whisker Plot Lowest = ?

Lower Quartile Value = ?

Median = ?

Upper Quartile Value = ?

Highest = ? Statistical Measures

Mean:

Median:

Mode: the average the middle score the most common score Calculating the Mean = Finding the Median = Sum of the scores

Number of scores _______________ Number of scores +1

2 _______________ Finding Median of odd number of scores If there are 3,5,7,9,11 etc. scores number of scores +1

2 Median = _______________ = 11+1

2 ___ = 6th score is the median Finding Median of even number of scores If there are 2,4,6,8,10 etc. scores Median = _______________ number of scores +1

2 = _____ 10+1

2 = the average of the 5th and 6th scores 5.5 6 Median = 5th score + 6th score

2 ____________ Questions: Exercise 9F - Stem-and-leaf plots

Questions: Odd Questions Only

1,3,5,7,9,11 1 3 Interquartile Range (IQR): Upper Quartile value - Lower Quartile value

Q - Q 1 3 Find the 5 Number Summary of the

following data sets: Question 1: Example: Question 2: Question 3: 33, 33, 36, 39, 40, 42, 43, 45, 46, 47, 50 1.2, 1.3, 1.5, 1.6, 1.6, 1.6, 1.8, 1.9, 2.0, 2.1, 2.2, 2.2, 2.3, 2.3, 2.5, 2.9, 3.0, 3.3, 3.7, 4.2 29, 33, 46, 49, 60, 62, 63, 95, 116, 147, 150 52.5, 56, 57.5, 58, 58.5, 58.5, 60.5, 61, 63,

78.5, 81, 83.5, 88, 88.5, 89.5, 90, 92.5, 93, 99 Highest:

Lowest: Highest:

Lowest: Highest:

Lowest: Highest:

Lowest: Median: Median: Median: Median: Upper Quartile (Q ):

Lower Quartile (Q ): Upper Quartile (Q ):

Lower Quartile (Q ): Upper Quartile (Q ):

Lower Quartile (Q ): Upper Quartile (Q ):

Lower Quartile (Q ): 1 1 1 1 3 3 3 3 Exercise 9G Questions 1-10 Chapter 9 Review Even Questions:

2,4,6,8,10,12 Misrepresentation of Data: To determine whether graphical data has been misrepresented, check: scale on both axes is linear

scales on vertical and horzontal axes have not been lengthened or shortened to give a biased impression

certain values have not been omitted in the graph

picture graphs are drawn to represent a height not a volume (goes up or down in equal amounts) (no missing values on the axes) (it is not a just part of the whole graph or has missing values) (the size of the picture is not proportional to it's reading on the

vertical axis) Changes of Scale Given Data of: By changing the vertical axis we can make the increase over the Year seem like a larger growth than it actually was. Omitting Values By omitting the values for April-June (A-J) it seems like the increase has been constant over the entire year Omitted A-J Value Another Example Which one would you use to support the notion that we are wasting tax payers money on police strength? Why? Showing a quicker increase (greater slope) Non-Linear Scale (different sized gaps) This graph has

even sized gaps Pictorial Representation The picture shows a larger growth than that of the vertical axis Exercise 9D

Even Questions