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Measures of Center in Statistics

Learn about measures of center in statistics, including the mean, median, and mode. Understand how to calculate and interpret these measures, and identify the best measure of center for different types of data.

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Measures of Center in Statistics

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  1. STATISTICS ELEMENTARY Section 2-4 Measures of Center MARIO F. TRIOLA EIGHTH EDITION

  2. a value at the center or middle of a data set Measures of Center

  3. Mean (Arithmetic Mean) AVERAGE the number obtained by adding the values and dividing the total by the number of values Definitions

  4.  denotes the addition of a set of values x is the variable usually used to represent the individual data values n represents the number of data values in a sample N represents the number of data values in a population Notation

  5. x x x = n Notation is pronounced ‘x-bar’ and denotes the mean of a set of sample values

  6. µis pronounced ‘mu’ and denotes the mean of all values in a population x x x = n x µ = N Notation is pronounced ‘x-bar’ and denotes the mean of a set of sample values Calculators can calculate the mean of data

  7. Median the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude Definitions • is not affected by an extreme value

  8. 7 3 4 5 3 6 3 3 4 5 6 7 no exact middle -- shared by two numbers (even number of values) 4 + 5 MEDIAN is 4.5 2

  9. 7 3 4 5 3 6 3 3 4 5 6 7 no exact middle -- shared by two numbers (even number of values) 4 + 5 MEDIAN is 4.5 2 7 3 4 5 3 6 8 3 3 4 5 6 7 8 exact middle -- odd number of values MEDIAN is 5

  10. Mode the score that occurs most frequently Bimodal – Two Modes Multimodal – Many Modes No Mode the only measure of central tendency that can be used with nominal data Definitions

  11. Mode is 5 Bimodal - 2 and 6 No Mode Examples a. 5 5 5 3 1 5 1 4 3 5 b. 1 2 2 2 3 4 5 6 6 6 7 9 c. 1 2 3 6 7 8 9 10

  12. Midrange - the value midway between the highest and lowest values in the original data set. Definitions highest score + lowest score Midrange= 2

  13. Carry one more decimal place than is present in the original set of values Round-off Rule for Measures of Center

  14. Best Measure of Center

  15. Symmetric Data is symmetric if the left half of its histogram is roughly a mirror of its right half. Skewed Data is skewed if it is not symmetric and if it extends more to one side than the other. Definitions

  16. Skewness Figure 2-13 (b) Mode = Mean = Median SYMMETRIC

  17. Skewness Figure 2-13 (b) Mode = Mean = Median SYMMETRIC Mean Mode Median Figure 2-13 (a) SKEWED LEFT (negatively)

  18. Skewness Figure 2-13 (b) Mode = Mean = Median SYMMETRIC Mean Mean Mode Mode Median Median Figure 2-13 (a) Figure 2-13 (c) SKEWED LEFT (negatively) SKEWED RIGHT (positively)

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