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Module 2
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- 1random variableis a mathematical function that may have more than one value Letters, such as x and y, are used to represent the values of random variables
- 2modeis the most frequently occurring observation in a data set. Some data sets have no mode while others have more than one mode. The problem with relying on the mode as a measure of central location is that it is not always unique and not always present.
- 3medianis the middle value in a data set that has its values arranged in order of magnitude. The median is the (N + 1) ÷ 2 value (where N = the number of observations in the ordered data set).
- 4arithmetic mean(usually referred to as simply the mean...aka Average) is the most widely used measure of central location. It is determined by finding the sum of all the observations in the data set and then dividing by the total number of observations.
- 5geometric mean (GM)measures the average rate of change (growth or decline) in a quantity. The formula for calculating the geometric mean is
Rg = [(1 + R1)(1 + R2) … (1 + Rn)]1/n – 1
where n = the number of growth factors - 6Rangemax value - min value
simple measure of the total spread of the data
(only looks at the extreme values) - 7variancemeasures how far individual values in the data set are spread out from the mean
2 important characteristics:
1. independent of the mean
2. measured in terms of squares of deviation - 8Empirical Rulecan be applied to a data set with a normal population (bell shaped histogram)
-mean is in the middle of the bell
- 68% fall within one standard deviation from the mean
- 95% fall within 2 standard deviations from the mean
- 99.7% fall within 3 sd from the mean - 9Chebysheff’s Theoremwhen the data set is not bell shaped,
According to Chebysheff, the fraction of all observations falling within k standard deviations of the mean is at least 1 – 1/k2 as long as k > 1.
For example, if k = 2, then the proportion of all observations falling within two standard deviations of the mean is at least 1 – 1/22 = 1 – 1/4 = 3/4, or 75% - 10oefficient of variationis a relative measure of variability that is expressed as a percentage rather than in terms of the units of the data set. CV measures the variability, σ, relative to the mean, µ.
=standard deviation/mean - 11standard deviationthe square root of the variance
unit of measure to determine how close/far away from the mean - 12inter-quartile rangethe difference between the third and first quartiles
- 13box plota pictorial representation fo the summary values in a data set. Includes:
smallest and largest values, the first and 3rd quartiles and the median. the box represents the inter-quartile range - 14an outlieris an unusually large or small individual item in the data set. Because it is so far removed from the other data, it is often questionable whether outliers are the result of an error in recording or measuring the data.
- 15Covariance:is a measure of how two variables change together
- 16coefficient of correlationto measure the degree of association between two variables
- 17The least squares methodis a means of plotting a straight line through the scatter points that best represents the linear relationship between the variables. While the coefficient of correlation explains the strength of the relationship, the least squares line tells you what the linear relationship is between the variables.
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- Professional Designation (Module 2: Summary Measures) QU1 Fichas sobre Module 2 , creado por jbbacik el 03/02/2015.
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