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Essential Question: Why is a knowledge of basic statistics helpful in real-world situations?. Statistics and Probability 13.1 Basic Statistics. 13-1: Basic Statistics. Population: The set of all people who can be chosen Sample: The set of people from the population who were actually chosen

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13 1 basic statistics
13-1: Basic Statistics
  • Population: The set of all people who can be chosen
  • Sample: The set of people from the population who were actually chosen
  • Example: Identify the population and the sample
    • There are three schedule options for classes at a high school: 90-minute classes every other day for a year, 90-minute classes every day for a semester or 45-minute classes every day for a year. Out of 1200 students, 50 students from each grade level are chosen at random and asked their preference.
      • Population:
      • Sample:

1200 students

50 students • 4 grades = 200 students

13 1 basic statistics1
13.1 Basic Statistics
  • Types of Data
    • Qualitative – categorical
    • Quantitative – numerical
      • Discrete – incremental
      • Continuous – no minimum difference
  • Example 1
    • The height of each player on a basketball team
    • The style of shoes worn by each student in a class
    • The number of people in each household in the US

Quantitative - continuous

Qualitative

Quantitative - discrete

13 1 basic statistics2
13.1 Basic Statistics
  • Data Displays
    • Frequency – number of times a value appears
    • Relative frequency – frequency/total number of items
  • Example 2/Example 3/Example 4
    • 30 people were asked their favorite flavor of ice cream: 6 vanilla, 12 chocolate, 4 butter pecan, 8 mint chocolate chip.
    • Display as a frequency table, bar graph, and pie chart
13 1 basic statistics4
13.1 Basic Statistics
  • Pie Chart
    • Each relative frequency takes a portion of 360˚
      • Vanilla: 0.2 ∙ 360˚ = 72˚
      • Chocolate: 0.4 ∙ 360˚ = 144˚
      • Butter pecan : 0.13 ∙ 360˚ ≈ 47˚
      • Mint chocolate chip: 0.27 ∙ 360˚ ≈ 97˚

Vanilla

20%

Mint Chocolate Chip

27%

Butter Pecan

13%

Chocolate

40%

13 1 basic statistics5
13.1 Basic Statistics
  • Displaying Quantitative Data
    • Curve types
      • Uniform – all values have approximately same frequency
      • Symmetric – right and left sides are mirror images
      • Skewed right – right side lower than the left side
      • Skewed left – left side lower than the right side
    • Skewed means “screwed”
    • Outlier – data far removed from the rest.
      • Usually the culprit in skewed data
13 1 basic statistics7
13.1 Basic Statistics
  • Example 5 - The shape of data
    • Choose the best determination of data (uniform, symmetric, skewed right, skewed left)
      • The last digit of each number in the phone book
      • The salaries of the employees of a corporation
      • The age of retirement for all people in the US
      • The height of all adult women in the US

Uniform

Skewed right

Skewed left

Symmetric

13 1 basic statistics8
13.1 Basic Statistics
  • Stem Plot
    • Choose leading digit(s) as stems
    • Arrange stems vertically
    • Last digit is the leaf
    • Provide a key
13 1 basic statistics9
13.1 Basic Statistics
  • 31 test scores on an exam
    • 32, 67, 89, 90, 87, 72, 75, 88, 95, 83, 97, 72, 85, 93, 79, 63, 70, 87, 74, 86, 98, 100, 97, 85, 77, 88, 92, 94, 81, 76, 64

3|2 = 32

13 1 basic statistics10
13.1: Basic Statistics
  • Assignment
    • Page 851
    • Problems:
      • 1 – 9 (all)
      • 11, 15
      • 19 – 24 (all)