1 / 30

Statistical Measures

Statistical Measures. Mrs. Watkins AP Statistics Chapters 5,6. MEASURES OF CENTER. Mean : arithmetic average of all data values population mean : sample mean : Formula : Mode : the most common value in a data set. Median : the middle value in a data set

Download Presentation

Statistical Measures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Statistical Measures Mrs. Watkins AP Statistics Chapters 5,6

  2. MEASURES OF CENTER Mean: arithmetic average of all data values population mean: sample mean: Formula: Mode: the most common value in a data set

  3. Median: the middle value in a data set Midrange: average of the extremes

  4. Trimmed Mean: when you find the mean of data set with a certain percentage of data values trimmed of the ends of the distribution Ex:

  5. 5 number summary 5 important numbers in data set: Min: Q1: Med: Q3: Max: Q1, Med, Q3, may not be actual data values

  6. BOXPLOT graphical display of data using 5 number summary (if outliers shown, called “modified box plot”)

  7. OUTLIERS Outliers: IQR Test for Outliers: (IQR )(1.5) = multiplier M Q1 - M = outlier lower bound Q3 + M = outlier upper bound If values exceed these bounds, they are outliers

  8. RESISTANCE Resistant Measures: Non-resistant Measures: Mean, Midrange: Median, IQR, Trimmed Mean:

  9. MEASURES OF SPREAD Range: the spread between high and low Resistant? IQR (Interquartile Range) : Resistant?

  10. STANDARD DEVIATION a measure of the average amount of deviation from the mean among the data values Population St. Deviation: Sample St. Deviation: We generally use sx because we usually do not have entire population.

  11. VARIANCE the square of the standard deviation what you get before taking square root Population Variance: Sample Variance: This measure not used much in elementary statistics but you need to know what it is.

  12. Coefficient of Variance measure of how relatively large a st. dev. is Ex: St. deviation of IQ = 15, Mean 100 St. deviation of height = 3 in, Mean 69

  13. “Comment on the distribution” You now have numbers to support your statements, rather than just graphs. SHAPE: OUTLIERS: CENTER: SPREAD: how widely does the data vary? Unusual Features: gaps, clusters

  14. SHAPE If the mean > median, then data distribution is skewed ________The mean is in the tail. If the mean < median, then data distribution is skewed ________The mean is in the tail. If the mean ≈ median, then data distribution is approximately ____________.

  15. SHAPE Symmetric if mean = median

  16. SKEWNESS Skewed left if mean < median Skewed right if mean > median Left Right Mean is in the tail of the data

  17. OTHER SHAPES Uniform distribution: allvalues relatively evenly distributed across interval Bimodal distribution: two peaks

  18. TRANSFORMATIONS TO DATA What would happen to the statistical measures if each data value had a constant added to or subtracted from it? Mean: Standard Deviation: Median: IQR:

  19. What would happen to the statistical measures if each data value had a constant multiplied or divided by it? Mean: Standard Deviation: Median: IQR:

  20. TRANSFORMATIONS TO DATA SET What would happen to the statistical measures if one very low or very high data value was added to the set? Mean: Standard Deviation: Median: IQR:

  21. MEASURES OF POSITION Give a numerical approximation of where a single data value stands compared to the whole distribution Quartiles: Percentiles: Z Scores:

  22. Z SCORES standardized score how a single value compares to entire data set in terms of position in distribution z=

  23. How unusual are you? Compute your z score for height? Compute your z score for Math SAT? Compute your z score for IQ?

  24. NORMAL MODEL shows how data is distributed symmetrically along an interval according to empirical rule Empirical Rule: of data within 1 st. deviation of μ of data within 2 st. deviations of μ of data within 3 st. deviations of μ

  25. ANOTHER OUTLIER TEST Using Empirical Rule: Data values of z > +2 st. deviations away from mean are mild outliers Data values of z > +3 st. deviations away from mean are extreme outliers

  26. NORMAL CURVE a theoretical ideal about how traits/characteristics are distributed Many human traits are approximately normally distributed such as height, body temp, IQ, pulse Avoid using “normal” when describing data—say “approximately normal or symmetric” unless clearly mound-shaped, bell-shaped

  27. NORMAL CURVE Normal curve—symmetric, mound-shaped Area under curve= A z score can be used to establish what % of the curve is less or more than the z score, and establish probability of a data value being in that position.

  28. FINDING PERCENTILE/PROBABILITY USING NORMAL CURVE • Calculate z score for data value • Use calculator: normalcdf under DISTR key Looking for area > z score: normalcdf (z, ∞) Looking for area < z score: normalcdf (∞, z) Looking for area between z scores: normalcdf (z1, z2)

  29. FINDING CUT OFF SCORES If you are given a percentile or probability, and need to determine the “cut off score” • Sketch curve to determine where z scoreis located. 2. Determine if you want area above or below this percentile 3. Use INVNORM on calculator invnorm(percentile)= z score • Use z score formula to solve for x.

  30. Does the data fit a normal model? • Check mean and median 2. Make a NORMAL PROBABILITY PLOT— 3. Make a BOXPLOT on calculator. AVOID using histograms on calculator to check.

More Related