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Week1&2 (1) - Weeks 1&2 Looking at Data...

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Weeks 1&2: Looking at Data - Distributions
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Weeks 1&2: Looking at Data - Distributions Introduction Individuals: objects described by a set of data (people, animals, or things) Variable: characteristic of an individual. It can take on different values for different individuals. (Examples: Age, Height, Gender, Favorite Class, Speed, Moisture, etc.) 2 / 49
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Weeks 1&2: Looking at Data - Distributions Variables Dataset After performing an experiment, survey or conducting a poll we have some information called a dataset . Example 1 : We asked several students what grade they earned in their math class and recorded their responses: A, C, D, A, A, B, C, C, B, A Example 2 : We measured the speed of cars at certain point of the highway: 66, 71, 25, 50, 45, 55, 69, 77, 80, 47, 100, 70 3 / 49
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Weeks 1&2: Looking at Data - Distributions Variables Samples In statistical language the datasets are called samples . Sample size, n , is the number of elements in a sample. Elements in a sample correspond to the values of a single variable. In Examples 1 and 2 the variables are the grade and the speed of the car. Sample sizes: n 1 = 10 , n 2 = 12 There are two main types of variables depending on what kind of values they take. 4 / 49
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Weeks 1&2: Looking at Data - Distributions Variables Type of Variables Quantitative: numeric values. They can be added, subtracted, averaged, etc. Discrete Variable - takes on values which are spaced. That is, for two adjacent values, there is no value that goes between them. Continuous Variable - values are all numbers in a given interval. That is, for two values of a continuous variable that are adjacent, there is another value that can go between the two. Categorical: an individual is placed into one of several groups or categories. These groups or categories are not usually numeric, although they may appear to be, and numeric functions don’t make sense. We will discuss these variables in Week 10. 5 / 49
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Weeks 1&2: Looking at Data - Distributions Variables Example Numeric Variable Discrete Continuous Categorical Length O Hours Enrolled O Major O Color of Eyes O 6 / 49
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Weeks 1&2: Looking at Data - Distributions Variables Distribution of Variables Every variable (quantitative or categorical) has a distribution of its values. The distribution of a variable tells us all possible values for the variable and how often that the variable takes these values. The distribution has three characteristics: shape, center and spread There are two ways to describe a distribution: with numbers - statistics with pictures - graphs The type of statistic or graph used depends on the type of variable. 7 / 49
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Weeks 1&2: Looking at Data - Distributions Variables Distribution of a Quantitive Variable Numeric example: the data below shows how much 50 consecutive shoppers spent in a particular store. 8 / 49
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Weeks 1&2: Looking at Data - Distributions Variables Distribution of a Quantitive Variable To describe the distribution of data we need 3 items: Shape: modes (peaks), symmetric or skewed Center: mean, median Spread: range, standard deviation, IQR The first thing you should always do (after you know what type of data you have) is plot the data.
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