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**Statistics and Probability 13.1 Basic Statistics**

Essential Question: Why is a knowledge of basic statistics helpful in real-world situations? Statistics and Probability 13.1 Basic Statistics

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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

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**13.1 Basic Statistics Types of Data Example 1**

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

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**13.1 Basic Statistics Data Displays Example 2/Example 3/Example 4**

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

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**13.1 Basic Statistics Flavor Frequency Relative Frequency Vanilla 6**

6/30 = 0.2 = 20% Chocolate 12 12/30 = 0.4 = 40% Butter pecan 4 4/30 ≈ 0.13 ≈ 13% Mint chocolate chip 8 8/30 ≈ 0.27 ≈27%

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**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%

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**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

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13.1 Basic Statistics

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**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

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**13.1 Basic Statistics Stem Plot Choose leading digit(s) as stems**

Arrange stems vertically Last digit is the leaf Provide a key

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**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 4 5 6 3 4 7 7 8 9 10 3|2 = 32

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**13.1: Basic Statistics Assignment Page 851 Problems: 1 – 9 (all)**

11, 15 19 – 24 (all)

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