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Session__4

Session__4 - Histogram for Quiz 1 Scores The distributions...

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Histogram for Quiz 1 Scores

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The distributions of many variables often follow a smooth bell-shaped curve, also known as the normal distribution.
When we collect data, the distribution may approximate, but never be identical to, the normal distribution. Even if a variable is normally distributed in the population, the observed distribution will never be exactly normal.

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Sampling error prohibits empirical distributions from being perfectly, mathematically normal, however, many empirical distributions will LOOK normal. Note that many variables may not be normally distributed (i.e. income, family size, level of education).
Theoretical distribution Empirical distribution

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The normal distribution has several important characteristics. 1. Symmetrical about the mean 2. Unimodal 3. Mean = median = mode
When you are describing a distribution, you should report information on 4 key characteristics: 1. Central tendency (mean, median, mode) 2. Variability (standard deviation) 3. Skewness 4. Kurtosis

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Review: Skewness refers to the degree of assymetry in a distribution. Formulas can be used to measure skewness. In a sample, these formulas are based on the distance from the mean to the median. A negatively skewed distribution will have a negative skewness index. A positively skewed distribution will have a positive skewness index.
Kurtosis indicates whether there are more or fewer extreme scores than expected in a normal distribution. Kurtosis measures “peakedness” in a distribution.

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Question: You get a score of 80 on a quiz. Did you do well? In order to answer this question, we need more information: Mean Standard deviation In order to make “raw scores” more meaningful, they can be transformed or standardized onto a different scale.

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X μ σ Normal Distribution μ = 0 σ = 1 Z Standardized Normal Distribution A standardized normal scale changes the scale of your variable to have μ = 0 and the standard deviation = 1. The standardized normal distribution is also called a Z-distribution
Every score in a distribution can be converted to a score on the standardized normal scale.

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Session__4 - Histogram for Quiz 1 Scores The distributions...

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