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Chapter 4 Comprehensive index

Chapter 4 Comprehensive index. Comprehensive index. From its roles and the angle of the method characteristics,comprehensive index can be summarized into three categories:. The conception and function of total amount index.

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Chapter 4 Comprehensive index

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  1. Chapter 4 Comprehensive index

  2. Comprehensive index From its roles and the angle of the method characteristics,comprehensive index can be summarized into three categories:

  3. The conception and function of total amount index • Total amount index is social economic phenomenon must reflect the time, the place, the total scale, under the condition of the level of statistics. • Total amount index form is JueDuiShu, may also display to absolute difference.

  4. Effect: • Total amount index can reflect a country's basic national conditions and National strength, reflect a department, unit and so on human, financial,The basic data of the content. • Total amount index is making decisions and the basis of scientific management. • Total amount index is the the foundation of calculated relative index and average index.

  5. Total amount index calculation • Calculation principle: • 1. The phenomenon of similar nature. • 2. Clear statistical meaning. • 3. Measurement unit shall be consistent.

  6. The concept of relative index • Opposite index is two contact index, the result of the numerical contrast reflects the number of things characteristics and quantity

  7. Opposite index role • Can the specific social and economic phenomenon that the proportion between the relationship. • Can make some can't direct comparison to find out the things together the basis of comparison • Opposite index is easy to remember, easy to confidential

  8. Structure relative index • 1. Can reflect the overall the internal structure of the features • 2. Through the different period of relative change, we can see that the changes of things process and its development trend • 3. Can reflect on the human, material and financial resources utilization degree and the production and business operation effect quality • 4. Structure in the application of the relative average

  9. Measures of Central Tendency Mean Arithmetic average Sum of all data values divided by the number of data values within the array Most frequently used measure of central tendency Strongly influenced by outliers- very large or very small values

  10. Measures of Central Tendency Determine the mean value of 48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55

  11. Measures of Central Tendency Median Data value that divides a data array into two equal groups Data values must be ordered from lowest to highest Useful in situations with skewed data and outliers (e.g., wealth management)

  12. Measures of Central Tendency Determine the median value of 48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55 Organize the data array from lowest to highest value. 59, 60, 62, 63, 63 58, 2, 5, 48, 49, 55, Select the data value that splits the data set evenly. Median = 58 What if the data array had an even number of values? 60, 62, 63, 63 58, 59, 5, 48, 49, 55,

  13. Measures of central tendency Usually the highest point of curve Mode Most frequently occurring response within a data array May not be typical May not exist at all Mode, bimodal, and multimodal

  14. Measures of Central Tendency Determine the mode of 48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55 Mode = 63 Determine the mode of 48, 63, 62, 59, 58, 2, 63, 5, 60, 59, 55 Mode = 63 & 59 Bimodal Determine the mode of 48, 63, 62, 59, 48, 2, 63, 5, 60, 59, 55 Mode = 63, 59, & 48 Multimodal

  15. Data Variation Measure of data scatter Range Difference between the lowest and highest data value Standard Deviation Square root of the variance Variance Average of squared differences between each data value and the mean

  16. Range Calculate by subtracting the lowest value from the highest value. Calculate the range for the data array. 2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63

  17. Standard Deviation • Calculate the mean . • Subtract the mean from each value. • Square each difference. • Sum all squared differences. • Divide the summation by the number of values in the array minus 1. • Calculate the square root of the product.

  18. Standard Deviation Calculate the standard deviation for the data array. 2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63 1. 2. 2 - 47.64 = -45.64 5 - 47.64 = -42.64 48 - 47.64 = 0.36 49 - 47.64 = 1.36 55 - 47.64 = 7.36 58 - 47.64 = 10.36 59 - 47.64 = 11.36 60 - 47.64 = 12.36 62 - 47.64 = 14.36 63 - 47.64 = 15.36 63 - 47.64 = 15.36

  19. Standard Deviation Calculate the standard deviation for the data array. 2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63 3. 11.362 = 129.05 12.362 = 152.77 14.362 = 206.21 15.362 = 235.93 15.362 = 235.93 -45.642 = 2083.01 -42.642 = 1818.17 0.362 = 0.13 1.362 = 1.85 7.362 = 54.17 10.362 = 107.33

  20. Standard Deviation Calculate the standard deviation for the data array. 2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63 4. 2083.01 + 1818.17 + 0.13 + 1.85 + 54.17 + 107.33 + 129.05 + 152.77 + 206.21 + 235.93 + 235.93 = 5,024.55 7. 5. 11-1 = 10 6. S = 22.42

  21. Variance Average of the square of the deviations • Calculate the mean. • Subtract the mean from each value. • Square each difference. • Sum all squared differences. • Divide the summation by the number of values in the array minus 1.

  22. Variance Calculate the variance for the data array. 2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63

  23. Graphing Frequency Distribution Numerical assignment of each outcome of a chance experiment A coin is tossed 3 times. Assign the variable X to represent the frequency of heads occurring in each toss. HHH X =1 when? 3 HHT 2 HTT,THT,TTH 2 HTH THH 2 1 HTT THT 1 TTH 1 0 TTT

  24. Graphing Frequency Distribution The calculated likelihood that an outcome variable will occur within an experiment HHH 3 0 HHT 2 2 HTH 1 THH 2 1 HTT 2 THT 1 TTH 1 3 0 TTT

  25. Graphing Frequency Distribution Histogram 0 1 2 x 3

  26. Histogram Open airplane passenger seats one week before departure What information does the histogram provide the airline carriers? What information does the histogram provide prospective customers?

  27. Measures of Central Tendency Determine the mean value of 48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55

  28. Measures of Central Tendency Median Data value that divides a data array into two equal groups Data values must be ordered from lowest to highest Useful in situations with skewed data and outliers (e.g., wealth management)

  29. Measures of Central Tendency Determine the median value of 48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55 Organize the data array from lowest to highest value. 58, 59, 60, 62, 63, 63 2, 5, 48, 49, 55, Select the data value that splits the data set evenly. Median = 58 What if the data array had an even number of values? 60, 62, 63, 63 58, 59, 5, 48, 49, 55,

  30. Measures of central tendency Usually the highest point of curve Mode Most frequently occurring response within a data array May not be typical May not exist at all Mode, bimodal, and multimodal

  31. Measures of Central Tendency Determine the mode of 48, 63, 62, 49, 58, 2, 63, 5, 60, 59, 55 Mode = 63 Determine the mode of 48, 63, 62, 59, 58, 2, 63, 5, 60, 59, 55 Mode = 63 & 59 Bimodal Determine the mode of 48, 63, 62, 59, 48, 2, 63, 5, 60, 59, 55 Mode = 63, 59, & 48 Multimodal

  32. Thanks for Your Attention

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