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Median quiz

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  • What is the first step in finding the median of a data set?
    The first step is to sort the data from smallest to largest.
  • How do you find the median when the data set has an odd number of values?
    The median is the middle value in the sorted data set.
  • How do you find the median when the data set has an even number of values?
    The median is the mean (average) of the two middle numbers in the sorted data set.
  • Why is the median considered a measure of center?
    Because it represents the middle value of a data set, summarizing the data with one central value.
  • What is a key advantage of using the median over the mean?
    The median is resistant to outliers, so extreme values do not significantly affect it.
  • What is a disadvantage of using the median?
    It only considers one or two values in the data set, so it may not reflect all the data.
  • What happens to the mean when an outlier is added to a data set?
    The mean can change significantly, being pulled toward the outlier.
  • What happens to the median when an outlier is added to a data set?
    The median changes very little or not at all, showing its resistance to outliers.
  • In what type of data distribution is the mean the best measure of center?
    The mean is best when the data is symmetric and has no outliers.
  • In what type of data distribution is the median the best measure of center?
    The median is best when the data is skewed or contains outliers.
  • What does it mean for a statistic to be 'resistant'?
    A resistant statistic is not significantly affected by extreme values or outliers.
  • Why is the median often used to report salaries instead of the mean?
    Because a few very high salaries can skew the mean, while the median better represents the typical salary.
  • If a data set is {3, 5, 10, 12, 14}, what is the median?
    The median is 10, the middle value after sorting.
  • If a data set is {3, 5, 10, 12, 14, 76}, what is the median?
    The median is 11, which is the average of the two middle numbers (10 and 12).
  • How does the presence of outliers affect the mean and median differently?
    Outliers can drastically change the mean but have little effect on the median.