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Median quiz #1

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  • How do you find the median of a set of numbers?
    To find the median, first sort the data from smallest to largest. If the number of data points is odd, the median is the middle value. If the number is even, the median is the mean (average) of the two middle values.
  • Why is the median considered a resistant measure of center?
    The median is resistant because it is not significantly affected by extreme values or outliers in the data set, unlike the mean, which can change drastically if outliers are present.
  • If a set of six ordered data values has a known median, how can you determine a missing value in the set?
    For six ordered values, the median is the mean of the third and fourth values. If the median and five of the six values are known, set up an equation where the average of the third and fourth values equals the median, and solve for the missing value.
  • What does the median represent in a set of numbers?
    The median represents the middle value of a sorted data set, dividing the data into two equal halves, with half the values below and half above.
  • What is the median of a single number, such as 1?
    The median of a single number is that number itself. For example, the median of the set {1} is 1.
  • What is the median of the set {0}?
    The median of the set {0} is 0.
  • What is the median of the numbers 1, 3, and 8?
    First, sort the numbers: 1, 3, 8. Since there are three numbers (an odd amount), the median is the middle value, which is 3.
  • What is the first step you must take before finding the median of a dataset?
    You must sort the data from smallest to largest before finding the median. This ensures you correctly identify the middle value or values.
  • How does the presence of an outlier affect the mean compared to the median?
    An outlier can drastically change the mean, pulling it toward the extreme value. The median, however, is much less affected and may only change slightly.
  • Why is the median often used to report salaries instead of the mean?
    The median is used because it better represents the typical value when there are a few extremely high salaries that would distort the mean. This makes the median a more accurate measure of central tendency for skewed distributions like income.
  • What is the median of the first nine positive integers?
    The median of the first nine positive integers (1, 2, 3, 4, 5, 6, 7, 8, 9) is 5, since it is the middle value when the numbers are arranged in order.
  • How can one determine the median of a data set?
    To determine the median of a data set, first sort the data from smallest to largest. If the number of data points is odd, the median is the middle value. If the number is even, the median is the average of the two middle values.
  • What is the median of the list: 2, 4, 6, 12, 14?
    The median of the list 2, 4, 6, 12, 14 is 6, as it is the middle value when the numbers are ordered.
  • Why is the median considered a resistant measure of center compared to the mean?
    The median is considered a resistant measure of center because it is not significantly affected by outliers or extreme values, whereas the mean can be greatly influenced by such values.