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Statistics

Statistics. Statistics. The collection, evaluation, and interpretation of data. Statistics. Statistics. Inferential Statistics Generalize and evaluate a population based on sample data. Descriptive Statistics Describe collected data. Data. Categorical or Qualitative Data.

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Statistics

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  1. Statistics

  2. Statistics The collection, evaluation, and interpretation of data

  3. Statistics Statistics Inferential Statistics Generalize and evaluate a population based on sample data Descriptive Statistics Describe collected data

  4. Data Categorical or Qualitative Data Values that possess names or labels Color of M&Ms, breed of dog, etc. Numerical or Quantitative Data Values that represent a measurable quantity Population, number of M&Ms, number of defective parts, etc.

  5. DataCollection Sampling Random Systematic Stratified Cluster Convenience

  6. Graphic Data Representation Histogram Frequency distribution graph Frequency Polygons Frequency distribution graph Bar Chart Categorical data graph Pie Chart Categorical data graph %

  7. 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

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

  9. 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)

  10. 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,

  11. Measures of Central Tendency Mode Most frequently occurring response within a data array • Usually the highest point of curve May not be typical May not exist at all Modal, bimodal, and multimodal

  12. 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

  13. Data Variation Measure of data scatter Range Difference between the lowest and highest data value Standard Deviation Square root of the variance

  14. 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

  15. Standard Deviation • s for a sample, not population • Calculate the mean • Subtract the mean from each value and then square it. • Sum all squared differences. • Divide the summation by the number of values in the array minus 1. • Calculate the square root of the product.

  16. 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)2 = 2083.01 (5 - 47.64)2 = 1818.17 (48 - 47.64)2 = 0.13 (49 - 47.64)2 = 1.85 (55 - 47.64)2 = 54.17 (58 - 47.64)2 = 107.33 (59 - 47.64)2 = 129.05 (60 - 47.64)2 = 152.77 (62 - 47.64)2 = 206.21 (63 - 47.64)2 = 235.93 (63 - 47.64)2 = 235.93

  17. 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 6. 5. s= 22.42

  18. 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

  19. 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

  20. Graphing Frequency Distribution Histogram 0 1 2 x 3

  21. Histogram Available airplane passenger seats one week before departure What information does the histogram provide the airline carriers? percent of the time What information does the histogram provide prospective customers? open seats

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