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What does Statistics Mean?

What does Statistics Mean?. Descriptive statistics Number of people Trends in employment Data Inferential statistics Make an inference about a population from a sample. Population Parameter Versus Sample Statistics. Population Parameter. Variables in a population

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What does Statistics Mean?

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  1. What does Statistics Mean? • Descriptive statistics • Number of people • Trends in employment • Data • Inferential statistics • Make an inference about a population from a sample

  2. Population Parameter Versus Sample Statistics

  3. Population Parameter • Variables in a population • Measured characteristics of a population • Greek lower-case letters as notation

  4. Sample Statistics • Variables in a sample • Measures computed from data • English letters for notation

  5. Making Data Usable • Frequency distributions • Proportions • Central tendency • Mean • Median • Mode • Measures of dispersion

  6. Frequency Distribution of Deposits Frequency (number of people making deposits Amount in each range) less than $3,000 499 $3,000 - $4,999 530 $5,000 - $9,999 562 $10,000 - $14,999 718 $15,000 or more 811 3,120

  7. Percentage Distribution of Amounts of Deposits Amount Percent less than $3,000 16 $3,000 - $4,999 17 $5,000 - $9,999 18 $10,000 - $14,999 23 $15,000 or more 26 100

  8. Probability Distribution of Amounts of Deposits Amount Probability less than $3,000 .16 $3,000 - $4,999 .17 $5,000 - $9,999 .18 $10,000 - $14,999 .23 $15,000 or more .26 1.00

  9. Measures of Central Tendency • Mean - arithmetic average • µ, Population; , sample • Median - midpoint of the distribution • Mode - the value that occurs most often

  10. Population Mean

  11. Sample Mean

  12. Number of Sales Calls Per Day by Salespersons Number of Salesperson Sales calls Mike 4 Patty 3 Billie 2 Bob 5 John 3 Frank 3 Chuck 1 Samantha 5 26

  13. Sales for Products A and B, Both Average 200 Product A Product B 196 150 198 160 199 176 199 181 200 192 200 200 200 201 201 202 201 213 201 224 202 240 202 261

  14. Measures of Dispersion or Spread • Range • Mean absolute deviation • Variance • Standard deviation

  15. The Range as a Measure of Spread • The range is the distance between the smallest and the largest value in the set. • Range = largest value – smallest value

  16. Deviation Scores • The differences between each observation value and the mean:

  17. Low Dispersion Verses High Dispersion 5 4 3 2 1 Low Dispersion Frequency 150 160 170 180 190 200 210 Value on Variable

  18. Low Dispersion Verses High Dispersion 5 4 3 2 1 High dispersion Frequency 150 160 170 180 190 200 210 Value on Variable

  19. AverageDeviation

  20. Mean Squared Deviation

  21. The Variance

  22. Variance

  23. Variance • The variance is given in squared units • The standard deviation is the square root of variance:

  24. Sample Standard Deviation

  25. Population Standard Deviation

  26. Sample Standard Deviation

  27. The Normal Distribution • Normal curve • Bell shaped • Almost all of its values are within plus or minus 3 standard deviations • I.Q. is an example

  28. Normal Distribution MEAN

  29. Normal Distribution 13.59% 13.59% 34.13% 34.13% 2.14% 2.14%

  30. Normal Curve: IQ Example 70 145 85 115 100

  31. Standardized Normal Distribution • Symetrical about its mean • Mean identifies highest point • Infinite number of cases - a continuous distribution • Area under curve has a probability density = 1.0

  32. Standard Normal Curve • Mean of zero, standard deviation of 1 • The curve is bell-shaped or symmetrical • About 68% of the observations will fall within 1 standard deviation of the mean • About 95% of the observations will fall within approximately 2 (1.96) standard deviations of the mean • Almost all of the observations will fall within 3 standard deviations of the mean

  33. A Standardized Normal Curve z 1 2 -2 -1 0

  34. The Standardized Normal is the Distribution of Z –z +z

  35. Standardized Scores

  36. Standardized Values • Used to compare an individual value to the population mean in units of the standard deviation

  37. Linear Transformation of Any Normal Variable Into a Standardized Normal Variable    X  Sometimes the scale is stretched Sometimes the scale is shrunk -2 -1 0 1 2

  38. Population distribution • Sample distribution • Sampling distribution

  39. Population Distribution    x

  40. Sample Distribution   X S

  41. Sampling Distribution

  42. Standard Error of the Mean • Standard deviation of the sampling distribution

  43. Central Limit TheoremThe theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

  44. Standard Error of the Mean

  45. Estimation of Parameter • Point estimates • Confidence interval estimates

  46. Confidence Interval

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