Bài giảng nguyên lý thông kê chương 3 numerical measures part a student

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Bài giảng nguyên lý thông kê chương  3 numerical measures part a student

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Chapter Statistical measures Measure center and location Measure variation/dispersion Summary Statistical measures Center and location Variation/Dispersion - Mean (arithmetic, weighted, geometric) - Range - Mode, Median - Percentile, Quartile - Variance - Standard deviation - Coefficient of variation Part A Measures of center and location Arithmetic mean Weighted mean Geometric mean Harmonic mean Median Mode Percentile, Quartile Arithmetic mean   The mean of a data set is the average of all the data values Arithmetic mean of a data set is defined as ‘ the sum of the values’ divided by the ‘number of values’ The sum of all values Arithmetic mean = The number of values Formula x1 + x2 + + xn x = n xi ∑ x = n where - x1 , x2 , , xn are the 1st x-value, 2nd xvalue, … nth x-value - n is the number of data values in the set Example  If a firm received orders worth: £151, £155, £160, £90, £270 for five consecutive months, their average value of orders per month would be calculated as: Limits of arithmetic mean Weighted mean  Simple frequency distribution  Grouped frequency distribution Weighted mean of a simple frequency distribution xi fi 10 12 13 14 16 17    Is the arithmetic mean appropriate to a simple frequency distribution? Why? Formula: n x f ∑ x = i =1n i f ∑ i= i i Example x f 12 18 30 20 15 Total 100 xf (x): Number of newspapers/magazines /journals a student read a week (f): Number of students Estimating the median graphically  Read at home 50% point Characteristics of the median Mode   The mode of a data set is the value which occurs most often or equivalently, has the largest frequency Example: The mode of the set 2, 3, 2, 4, 5, 2, is: The mode of a simple frequency distribution  Mode is the value which has the largest frequency Mode? xi fi 10 15 17 20 18 The mode of a grouped frequency distribution   Step 1: Find the modal class Step 2: Estimate the mode by the formula M = LM + cM LM cM f M − f M −1 ( f M − f M −1 ) + ( f M − f M +1 ) Lower limit of modal class Modal class width fM0 Frequency of modal class f M −1 Frequency of the class immediately prior to the modal class fM0 +1 Frequency of the class immediately following to the modal class Example  Amount of food per person in province A Amount of food (kg/person) 400-500 Number of people 500-600 30 600-700 45 700-800 80 800-900 30 900-1000 Mode? 10 Modal class? Amount of food (kg/person) Number of people 400-500 10 500-600 30 600-700 45 700-800 80 800-900 30 900-1000 Estimate the Mode by the formula Graphical estimation of the mode Characteristics of the mode Graphical comparison of mean, median and mode  Symmetric Relative Frequency 35 30 25 20 15 10 05 Mean Median Mode Graphical comparison of mean, median and mode Moderately Skewed Left 35 Relative Frequency  30 25 20 15 10 05 Mean Median Mode Graphical comparison of mean, median and mode Moderately Right Skewed 35 Relative Frequency  30 25 20 15 10 05 Mode Median Mean Graphical comparison of mean, median and mode Highly Skewed Right 35 Relative Frequency  30 25 20 15 10 05 Percentile and quartile  Read at home

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Mục lục

  • Chapter 3 Statistical measures

  • Summary

  • Part A Measures of center and location

  • 1. Arithmetic mean

  • Formula

  • Example

  • Limits of arithmetic mean

  • 2. Weighted mean

  • Weighted mean of a simple frequency distribution

  • Slide 10

  • Weighted mean of a simple frequency distribution

  • Weighted mean of a grouped frequency distribution

  • Slide 13

  • Slide 14

  • Slide 15

  • 3. Geometric mean

  • Slide 17

  • Slide 18

  • Slide 19

  • Slide 20

  • Slide 21

  • Slide 22

  • Slide 23

  • Slide 24

  • Slide 25

  • Slide 26

  • Slide 27

  • 4. Harmonic mean

  • Characteristics of the mean

  • 5. Median

  • Notes

  • Median for a simple frequency distribution

  • Slide 33

  • Slide 34

  • Median for a grouped frequency distribution

  • Slide 36

  • Slide 37

  • Slide 38

  • Estimating the median graphically

  • Characteristics of the median

  • 6. Mode

  • The mode of a simple frequency distribution

  • The mode of a grouped frequency distribution

  • Slide 44

  • Slide 45

  • Estimate the Mode by the formula

  • Graphical estimation of the mode

  • Characteristics of the mode

  • Slide 49

  • Graphical comparison of mean, median and mode

  • Slide 51

  • Slide 52

  • 7. Percentile and quartile

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