stat1.pptx
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The document discusses various quantitative techniques for summarizing data, including measures of central tendency (mean, median, mode) and dispersion (range, quartiles, standard deviation). It provides formulas for calculating the mean, median, mode, variance and standard deviation. An example is given of calculating the mean from a table of dice roll results.
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Measuring the Dispersion of Data
Quartiles, outliers and boxplots
Quartiles: Q1 (25th percentile), Q3 (75th percentile)
Inter-quartile range: IQR = Q3 Q1
Five number summary: min, Q1, median, Q3, max
Boxplot: ends of the box are the quartiles; median is marked; add whiskers,
and plot outliers individually
Outlier: usually, a value higher/lower than 1.5 x IQR
Variance and standard deviation (sample: s, population: )
Variance: (algebraic, scalable computation)
Standard deviation s (or ) is the square root of variance s2 (or 2)
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stat1.pptx
- 2. Mean, Median, Mode and Range The mean, median and mode are types of average. The range gives a measure of the spread of a set of data
- 6. Finding the mean from a table of data Example A dice was rolled 20 times. On each roll the dice shows a value from 1 to 6. The results have been recorded in the table below: FIND MEAN
- 7. divide the total of all the data values by the number of data values. In this case you need to divide 68 by 20, giving 3.4.
- 11. 11 Measuring the Central Tendency Mean (algebraic measure) (sample vs. population): Note: n is sample size and N is population size. Weighted arithmetic mean: Trimmed mean: chopping extreme values Median: Middle value if odd number of values, or average of the middle two values otherwise Estimated by interpolation (for grouped data): Mode Value that occurs most frequently in the data Unimodal, bimodal, trimodal Empirical formula: n i i x n x 1 1 n i i n i i i w x w x 1 1 width freq freq n L median median l ) ) ( 2 / ( 1 ) ( 3 median mean mode mean N x Median interval
- 12. October 25, 2022 Data Mining: Concepts and Techniques 12 Symmetric vs. Skewed Data Median, mean and mode of symmetric, positively and negatively skewed data positively skewed negatively skewed symmetric
- 13. 13 Measuring the Dispersion of Data Quartiles, outliers and boxplots Quartiles: Q1 (25th percentile), Q3 (75th percentile) Inter-quartile range: IQR = Q3 Q1 Five number summary: min, Q1, median, Q3, max Boxplot: ends of the box are the quartiles; median is marked; add whiskers, and plot outliers individually Outlier: usually, a value higher/lower than 1.5 x IQR Variance and standard deviation (sample: s, population: ) Variance: (algebraic, scalable computation) Standard deviation s (or ) is the square root of variance s2 (or 2) n i n i i i n i i x n x n x x n s 1 1 2 2 1 2 2 ] ) ( 1 [ 1 1 ) ( 1 1 n i i n i i x N x N 1 2 2 1 2 2 1 ) ( 1
- 23. Formula for mode