AP Stats: Chapter 2

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AP Stats: Chapter 2
2013-10-15 22:26:47
Modeling Data Distributions

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  1. percentile implication
    if someone scored at the 93rd percentile, that means that in the distribution, 93% of the people earned that score or less
  2. how to calculate percentile from data
    (number of scores below the score) / (total number of scores)
  3. cumulative relative frequency graph
    used to examine a location within a distribution. Groups the observations into equal-width classes, shows accumulating percent of observations as you move through the classes in increasing order
  4. how to calculate relative frequency
    (frequency)/(total frequencies) x100
  5. how to calculate cumulative frequency
    (frequency) + (frequencies below this frequency)
  6. how to calculate cumulative relative frequency
    (cumulative frequency)/(total frequencies)
  7. cumulative relative frequency graph aka ogive
  8. interpretation of cumulative relative frequency
    percentage represents the amount of people at that class or lower
  9. ogive
    aka cumulative relative frequency graph
  10. how to calculate z-scores
  11. effect of adding or subtracting a constant
    • adds a to the center and location (mean, median, quartiles, percentiles)
    • does not affect shape or measures of spread (range, IQR, standard deviation)
  12. effect of multiplying or dividing by a constant
    • multiplies/divides measures of center and location by b (mean, median, quartiles, percentiles)
    • multiplies/divides measures of spread by |b| (range, IQR, standard deviation)
    • multiplies/divides the variance by b2
    • does not change shape
  13. density curve
    • a curve that is always on or above the horizontal axis and has exactly 1 area underneath it
    • describes the overall pattern of a distribution
  14. median of a density curve
    point with half the area under the curve to its left and  the remaining half of the area to its right, divides the area of the density curve in half
  15. mean of a density curve
    the point at which the curve would balance if made of solid material
  16. normal distribution
    • described by the normal density curve, specified by the mean and standard deviation N (μ, σ)
    • mean is at the center of the symmetric normal curve, standard deviation is the distance from the center to the change-of-curvature points on each side
  17. inflection point
    point where the curve changes shape; where the curve changes from a right-side up U to an upside down U
  18. common examples of normal distributions
    • scores on tests taken by many people
    • repeated careful measurement of same quantity
    • characteristics of biological populations
  19. 68-95-99.7 Rule
  20. Chebyshev's inequality
    in any distribution, the proportion of observations falling within k standard deviations of the mean is at least
  21. standard normal distribution
    normal distribution with a mean 0 and standard deviation 1
  22. standard normal distribution
  23. standard normal table
    table of areas under the standard normal curve; table entry for each value z is the area to the left of z; shown in Table A
  24. normal probability plot
  25. normal probability plot
    used to assess whether a data set follows a normal distribution
  26. how to use a normal probability plot to tell if something is a normal distribution
    • normal if points lie close to a straight line
    • clear departures from normality indicate that the data is not normal
  27. normal cdf
    calculator function used to find the area of a normal distribution when you have the cutoff points
  28. invnorm
    calculator function used to find the associated cutoff points when you have the area

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