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Statistics

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The collection, evaluation, and interpretation of data

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

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

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Data Collection Sampling Random Systematic Stratified Cluster Convenience

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

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

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

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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)

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

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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 Modal, bimodal, and multimodal

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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

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

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

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Standard Deviation σ for a sample, not population 1.Calculate the mean 2. Subtract the mean from each value and then square it. 3.Sum all squared differences. 4. Divide the summation by the number of values in the array minus 1. 5. Calculate the square root of the product.

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Standard Deviation 2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63 Calculate the standard deviation for the data array. 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

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Standard Deviation 2, 5, 48, 49, 55, 58, 59, 60, 62, 63, 63 Calculate the standard deviation for the data array. 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 5. 6. S = 22.42

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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. Toss OutcomeX Value HHH HHT HTH THH HTT THT TTH TTT 3 2 2 2 1 1 1 0 X =1 when? HTT,THT,TTH

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Graphing Frequency Distribution The calculated likelihood that an outcome variable will occur within an experiment Toss OutcomeX value HHH HHT HTH THH HTT THT TTH TTT 3 2 2 2 1 1 1 0 xP(x) 0 1 2 3

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Graphing Frequency Distribution xP(x) 0 1 2 3 x Histogram

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

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