AICP Statistics
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| Descriptive Statistics | characteristics of a population
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| Inferential Statistics | determine characteristics of a population based on observations made on a sample from that population. We infer things about the population based on what is observed in the sample.
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| Mean | the average of a distribution. The mean of [2, 3, 4, 5] is 3.5.
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| Median | is the middle number of a ranked distribution. The median of [2, 3, 4, 6, 7] is 4.
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| Mode | the most frequent number in a distribution. The modes of [1, 2, 3, 3, 5, 6, 7, 7] are 3 and 7. There can be more than one mode for a data set.
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| Nominal Data | classified into mutually exclusive groups that lack intrinsic order. Race, social security number, and sex are examples of nominal data. Mode is the only measure of central tendency that can be used for nominal data.
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| Ordinal Dana | has values that are ranked so that inferences can be made regarding the magnitude. Hhas no fixed interval between values (educational attainment, letter grade on a test are ). Mode and median are used for ordinal data
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| Interval Data | data that has an ordered relationship with a magnitude. For temperature, 30 degrees is not twice as cold as 60 degrees. Mean is the best measure of interval data. Where the data is skewed median can be used.
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| Ratio Data | s an ordered relationship and equal intervals. Distance is an example of ratio data because 3.2 miles is twice as long as 1.6 miles. Any form of central tendency can be used for this type of data.
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| Normal Distribution | one that is symmetrical around the mean. This is a bell curve.
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| Distribution Skewed to the Right | has a few high numbers (outliers) that pull the mean to the right. For example, if there are three $20 million homes in your community, it is likely to skew the mean home value to the right.
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| Distribution Skewed to the Left | has a few low numbers (outliers) that pull the mean to the left. When taking the AICP exam, for instance, a few people may give up and walk out resulting in a few very low scores, which would skew the mean score to the left.
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| Range | simplest measure of dispersion. The range is the difference between the highest and lowest scores in a distribution. The age range of the respondents in a neighborhood survey goes from 18-year-old to 62-year-old. This results in a range of 44.
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| Variance | average squared difference of scores from the mean score of a distribution.Variance is a descriptor of a probability distribution, how far the numbers lie from the mean.
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| Standard Deviation | square root of the variance. if we want to know the difference in wages, we need to calculate the mean, variance, and standard deviation. If the employees earn $10, $20, and $35 per hour, the mean is $21.67.
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| Standard Error | standard deviation of a sampling distribution. Standard errors indicate the degree of sampling fluctuation. The larger the sample size the smaller the standard error
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| Confidence Interval | an estimated range of values which is likely to include an unknown population parameter. The width of the confidence interval gives us an idea of how uncertain we are about the unknown parameter. A wide interval may indicate that we need more data.
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| Chi Square | non-parametric test statistic that provides a measure of the amount of difference between two frequency distributions. Commonly used for probability distributions in inferential statistics.
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