Chapter 8 making sense of sample data
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This document provides information about organizing and summarizing data. It discusses discrete and continuous data and how to represent each using frequency tables, graphs, and other visualizations. Discrete data examples include the number of fraudulent cheques received each week and eye color in a class. Continuous data examples include truck weights and the value of life insurance policies over time. Methods for organizing data include frequency tables, histograms, pie charts, bar graphs, stem-and-leaf plots and ogives. The document also includes examples and explanations of key terminology used in statistics.
Chapter 8 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