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2013/05/07
1
STATISTICS
X-Kit Textbook
Chapter 8 (Making sense of Sample Data)
Precalculus Textbook
Appendix B: Concepts in Statistics
Par B.1 (Representing Data)
ORGANISE& SUMMARISERAW DATA
Raw Data
Discrete Data
Ungrouped
Frequency
Table
Grouped (low
frequency)
Continuous
Data
Grouped
Frequency
Table
Number of fraudulent cheques receivedat a
bank each week for 30 weeks
Week
1
2 3 4 5 6 7 8 9 10
5 3 8 3 3 1 10 4 6 8
Week
11
12 13 14 15 16 17 18 19 20
3 5 4 7 6 6 9 3 4 5
Week
21
22 23 24 25 26 27 28 29 30
7 9 4 5 8 6 4 4 10 4
DISCRETEDATA
TERMINOLOGY EXPLANATION
Variable of Interest? It is the number of fraudulent cheques
in a week.
Continuous or Discrete
Data?
Discrete Data because cheques can only
exist in whole numbers.
Raw Data? A list of different values. Data has not
been processed in any way.
Data Point or Observation? Each of the values in the raw data.
Frequency? The number of times a data value
appears.
Frequency Table Table to organise and summarise data.
FREQUENCYTABLE
Distinct Values Tally Marks Frequency
1 / 1
2 0
3 //// 5
4 //// // 7
5 //// 4
6 //// 4
7 // 2
8 /// 3
9 // 2
10 // 2
GRAPH
0
1
2
3
4
5
6
7
8
1 2 3 4 5 6 7 8 9 10
Frequency
Frequency
2013/05/07
2
Truck Data: weights(in tonnes) of 20 fully
loaded trucks
Truck
1
2 3 4 5 6 7 8 9 10
Weight
4.54
3.81 4.29 5.16 2.51 4.63 4.75 3.98 5.04 2.80
Truck
11
12 13 14 15 16 17 18 19 20
Weight
2.52
5.88 2.95 3.59 3.87 4.17 3.30 5.48 4.26 3.53
CONTINUOUSDATA
TERMINOLOGY EXPLANATION
Variable of Interest? The weight of a loaded truck.
Continuous or Discrete
Data?
Continuous Data, you can get any
number of values between two
given values.
Frequency Table Table to organise and summarise
data.
Grouped Frequency Table
FREQUENCYTABLE
Class Intervals Tally Marks Frequency
𝟐. 𝟓 ≤ 𝒙 ≤ 𝟑. 𝟎 //// 4
𝟑. 𝟎 ≤ 𝒙 ≤ 𝟑. 𝟓 / 1
𝟑. 𝟓 ≤ 𝒙 ≤ 𝟒. 𝟎 //// 5
𝟒. 𝟎 ≤ 𝒙 ≤ 𝟒. 𝟓 /// 3
𝟒. 𝟓 ≤ 𝒙 ≤ 𝟓. 𝟎 /// 3
𝟓. 𝟎 ≤ 𝒙 ≤ 𝟓. 𝟓 // 2
𝟓. 𝟓 ≤ 𝒙 ≤ 𝟔. 𝟎 // 2
GRAPH
0
1
2
3
4
5
6
0 - 2.5 2.5 - 3.0 3.0 - 3.5 3.5 - 4.0 4.0 - 4.5 4.5 - 5.0 5.0 - 5.5 5.5 - 6.0
Frequency
Frequency
PRESENTATIONOF DATA
Frequency
Table
Pictogram
Bar
Graphs
Histogram
Pie
Chart
Line
Graphs
Stem-and-
Leaf
Ogive
FREQUENCYTABLE
Class Intervals Frequency Cumulative
Frequency
𝟐. 𝟓 ≤ 𝒙 ≤ 𝟑. 𝟎 4 4
𝟑. 𝟎 ≤ 𝒙 ≤ 𝟑. 𝟓 1 5
𝟑. 𝟓 ≤ 𝒙 ≤ 𝟒. 𝟎 5 10
𝟒. 𝟎 ≤ 𝒙 ≤ 𝟒. 𝟓 3 13
𝟒. 𝟓 ≤ 𝒙 ≤ 𝟓. 𝟎 3 16
𝟓. 𝟎 ≤ 𝒙 ≤ 𝟓. 𝟓 3 19
𝟓. 𝟓 ≤ 𝒙 ≤ 𝟔. 𝟎 1 20
2013/05/07
3
OGIVE
0
5
10
15
20
25
2.5 3 3.5 4 4.5 5 5.5 6
Cumulative Frequency
Cumulative Frequency
Pictogram: Net Worthof America'sRichest Billionaires
Pie Chart: Average Annual Expenses in a U.S. Household
EXAMPLE
In a class with 30 pupils there are 12 with
blue eyes; 9 with brown eyes; 4 with dark
brown eyes and 5 with green eyes.
1. Draw a pie chart showing this
information.
2. Calculate the fraction and percentage
represented by each eye colour.
EXAMPLE: SOLUTION
Colour of
Eyes
Frequency Angle at Centre Percentage
Blue 12 𝟏𝟐
𝟑𝟎
× 𝟑𝟔𝟎°
= 𝟏𝟒𝟒°
𝟏𝟐
𝟑𝟎
× 𝟏𝟎𝟎 = 𝟒𝟎%
Brown 9 𝟗
𝟑𝟎
× 𝟑𝟔𝟎°
= 𝟏𝟎𝟖°
𝟗
𝟑𝟎
× 𝟏𝟎𝟎 = 𝟑𝟎%
Dark Brown 4 𝟒
𝟑𝟎
× 𝟑𝟔𝟎°
= 𝟒𝟖°
𝟒
𝟑𝟎
× 𝟏𝟎𝟎 = 𝟏𝟑, 𝟑%
Green 5 𝟓
𝟑𝟎
× 𝟑𝟔𝟎°
= 𝟔𝟎°
𝟓
𝟑𝟎
× 𝟏𝟎𝟎 = 𝟏𝟔, 𝟕%
Total 30 𝟑𝟔𝟎° 𝟏𝟎𝟎%
PIE CHART
Blue
Brown
Dark Brown
Green
2013/05/07
4
Bar Graph: Expected U.S. PopulationAged 100 and Over DoubleBar Graph: Fuel Efficiency
LineGraph: Effectof Inflationon the Valueof a $100,000
LifeInsurance Policy
DoubleLineGraph: Populationsof Californiaand Texas
Stem-and-Leaf Plot
Represent the data below in a stem-and-leaf plot:
152; 165; 143; 139; 138;
144; 150; 158; 161; 157;
143; 156; 162; 165; 139;
158; 151; 167; 166; 160;
170; 132; 145; 151; 148;
147; 171; 155; 146; 141.
Stem-and-Leaf Plot
STEM LEAVES
13 9; 8; 9; 2
14 3; 4; 3; 5; 8; 7; 6; 1
15 2; 0; 8; 7; 6; 8; 1; 1; 5
16 5; 1; 2; 5; 7; 6; 0
17 0; 1

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Making Sense of Sample Data

  • 1. 2013/05/07 1 STATISTICS X-Kit Textbook Chapter 8 (Making sense of Sample Data) Precalculus Textbook Appendix B: Concepts in Statistics Par B.1 (Representing Data) ORGANISE& SUMMARISERAW DATA Raw Data Discrete Data Ungrouped Frequency Table Grouped (low frequency) Continuous Data Grouped Frequency Table Number of fraudulent cheques receivedat a bank each week for 30 weeks Week 1 2 3 4 5 6 7 8 9 10 5 3 8 3 3 1 10 4 6 8 Week 11 12 13 14 15 16 17 18 19 20 3 5 4 7 6 6 9 3 4 5 Week 21 22 23 24 25 26 27 28 29 30 7 9 4 5 8 6 4 4 10 4 DISCRETEDATA TERMINOLOGY EXPLANATION Variable of Interest? It is the number of fraudulent cheques in a week. Continuous or Discrete Data? Discrete Data because cheques can only exist in whole numbers. Raw Data? A list of different values. Data has not been processed in any way. Data Point or Observation? Each of the values in the raw data. Frequency? The number of times a data value appears. Frequency Table Table to organise and summarise data. FREQUENCYTABLE Distinct Values Tally Marks Frequency 1 / 1 2 0 3 //// 5 4 //// // 7 5 //// 4 6 //// 4 7 // 2 8 /// 3 9 // 2 10 // 2 GRAPH 0 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 10 Frequency Frequency
  • 2. 2013/05/07 2 Truck Data: weights(in tonnes) of 20 fully loaded trucks Truck 1 2 3 4 5 6 7 8 9 10 Weight 4.54 3.81 4.29 5.16 2.51 4.63 4.75 3.98 5.04 2.80 Truck 11 12 13 14 15 16 17 18 19 20 Weight 2.52 5.88 2.95 3.59 3.87 4.17 3.30 5.48 4.26 3.53 CONTINUOUSDATA TERMINOLOGY EXPLANATION Variable of Interest? The weight of a loaded truck. Continuous or Discrete Data? Continuous Data, you can get any number of values between two given values. Frequency Table Table to organise and summarise data. Grouped Frequency Table FREQUENCYTABLE Class Intervals Tally Marks Frequency 𝟐. 𝟓 ≤ 𝒙 ≤ 𝟑. 𝟎 //// 4 𝟑. 𝟎 ≤ 𝒙 ≤ 𝟑. 𝟓 / 1 𝟑. 𝟓 ≤ 𝒙 ≤ 𝟒. 𝟎 //// 5 𝟒. 𝟎 ≤ 𝒙 ≤ 𝟒. 𝟓 /// 3 𝟒. 𝟓 ≤ 𝒙 ≤ 𝟓. 𝟎 /// 3 𝟓. 𝟎 ≤ 𝒙 ≤ 𝟓. 𝟓 // 2 𝟓. 𝟓 ≤ 𝒙 ≤ 𝟔. 𝟎 // 2 GRAPH 0 1 2 3 4 5 6 0 - 2.5 2.5 - 3.0 3.0 - 3.5 3.5 - 4.0 4.0 - 4.5 4.5 - 5.0 5.0 - 5.5 5.5 - 6.0 Frequency Frequency PRESENTATIONOF DATA Frequency Table Pictogram Bar Graphs Histogram Pie Chart Line Graphs Stem-and- Leaf Ogive FREQUENCYTABLE Class Intervals Frequency Cumulative Frequency 𝟐. 𝟓 ≤ 𝒙 ≤ 𝟑. 𝟎 4 4 𝟑. 𝟎 ≤ 𝒙 ≤ 𝟑. 𝟓 1 5 𝟑. 𝟓 ≤ 𝒙 ≤ 𝟒. 𝟎 5 10 𝟒. 𝟎 ≤ 𝒙 ≤ 𝟒. 𝟓 3 13 𝟒. 𝟓 ≤ 𝒙 ≤ 𝟓. 𝟎 3 16 𝟓. 𝟎 ≤ 𝒙 ≤ 𝟓. 𝟓 3 19 𝟓. 𝟓 ≤ 𝒙 ≤ 𝟔. 𝟎 1 20
  • 3. 2013/05/07 3 OGIVE 0 5 10 15 20 25 2.5 3 3.5 4 4.5 5 5.5 6 Cumulative Frequency Cumulative Frequency Pictogram: Net Worthof America'sRichest Billionaires Pie Chart: Average Annual Expenses in a U.S. Household EXAMPLE In a class with 30 pupils there are 12 with blue eyes; 9 with brown eyes; 4 with dark brown eyes and 5 with green eyes. 1. Draw a pie chart showing this information. 2. Calculate the fraction and percentage represented by each eye colour. EXAMPLE: SOLUTION Colour of Eyes Frequency Angle at Centre Percentage Blue 12 𝟏𝟐 𝟑𝟎 × 𝟑𝟔𝟎° = 𝟏𝟒𝟒° 𝟏𝟐 𝟑𝟎 × 𝟏𝟎𝟎 = 𝟒𝟎% Brown 9 𝟗 𝟑𝟎 × 𝟑𝟔𝟎° = 𝟏𝟎𝟖° 𝟗 𝟑𝟎 × 𝟏𝟎𝟎 = 𝟑𝟎% Dark Brown 4 𝟒 𝟑𝟎 × 𝟑𝟔𝟎° = 𝟒𝟖° 𝟒 𝟑𝟎 × 𝟏𝟎𝟎 = 𝟏𝟑, 𝟑% Green 5 𝟓 𝟑𝟎 × 𝟑𝟔𝟎° = 𝟔𝟎° 𝟓 𝟑𝟎 × 𝟏𝟎𝟎 = 𝟏𝟔, 𝟕% Total 30 𝟑𝟔𝟎° 𝟏𝟎𝟎% PIE CHART Blue Brown Dark Brown Green
  • 4. 2013/05/07 4 Bar Graph: Expected U.S. PopulationAged 100 and Over DoubleBar Graph: Fuel Efficiency LineGraph: Effectof Inflationon the Valueof a $100,000 LifeInsurance Policy DoubleLineGraph: Populationsof Californiaand Texas Stem-and-Leaf Plot Represent the data below in a stem-and-leaf plot: 152; 165; 143; 139; 138; 144; 150; 158; 161; 157; 143; 156; 162; 165; 139; 158; 151; 167; 166; 160; 170; 132; 145; 151; 148; 147; 171; 155; 146; 141. Stem-and-Leaf Plot STEM LEAVES 13 9; 8; 9; 2 14 3; 4; 3; 5; 8; 7; 6; 1 15 2; 0; 8; 7; 6; 8; 1; 1; 5 16 5; 1; 2; 5; 7; 6; 0 17 0; 1