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Comparing Distributions - Pre Algebra

  1. Which measures of center and spread are best for comparing distributions that are skewed or have outliers?
    The median and the IQR, because neither is strongly affected by extreme values.
  2. How can the difference between two means be expressed as a multiple of variability?
    Divide the difference in means by the MAD (when the two MADs are similar). A larger result means less overlap.
  3. Which measures of center and spread are typically used to compare roughly symmetric distributions without outliers?
    The mean and the mean absolute deviation (MAD).
  4. Class A has median score 78 with IQR 10. Class B has median 85 with IQR 10. What is the best comparison?
    Class B typically scored 7 points higher, and the two classes have the same spread.
  5. Two groups have means 20 and 26, and both have MAD 3. How many MADs apart are the means?
    2 MADs. The difference is 26−20=626 - 20 = 6, and 6÷3=26 \div 3 = 2.
  6. Two teams both have a mean height of 60 inches. Team A has MAD 2 inches and Team B has MAD 5 inches. Which team's heights are more consistent?
    Team A. Its smaller MAD means heights are closer to the mean.
  7. Which two features should be described when comparing two numerical distributions?
    Their centers (such as mean or median) and their spreads (such as MAD or IQR).
  8. Why compare medians instead of means when one group contains an extreme outlier?
    The median is resistant to outliers, while the mean is pulled toward the extreme value.
  9. What does a larger IQR in one of two groups indicate?
    The middle half of that group's data is more spread out, so its values are less consistent.
  10. Group A's values range from 40 to 60, and Group B's values range from 70 to 90. How do the distributions overlap?
    They do not overlap. Every value in Group B is greater than every value in Group A.
  11. Store A wait times have median 5 minutes and IQR 6 minutes. Store B has median 5 minutes and IQR 2 minutes. Which store's waits are more predictable?
    Store B. The typical waits are equal, but B's smaller IQR means its middle half of waits varies less.

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