Ask Question
13 June, 19:08

Here are the summary statistics for the weekly payroll of a small company: lowest salaryequals= $250250 , mean salaryequals= $900900 , medianequals= $800800 , rangeequals= $10001000 , IQRequals= $700700 , first quartileequals= $450450 , standard deviationequals= $400400. a) Do you think the distribution of salaries is symmetric, skewed to the left, or skewed to the right? Explain why. A. The distribution is symmetricsymmetric because the mean is greater thangreater than the median. B. The distribution is skewed to the leftskewed to the left because the mean is greater thangreater than the median. C. The distribution is skewed to the rightskewed to the right because the mean is greater thangreater than the median. Your answer is correct. D. There is not enough information to estimate the shape of the distribution. b) Between what two values are the middle 50% of the salaries found?

+1
Answers (1)
  1. 13 June, 19:24
    0
    a) The distribution is skewed to the right because the mean is greater than the median.

    b) The middle 50% of the values lie between $ 450 and $ 1150

    Step-by-step explanation:

    Following data about the distribution is available:

    Lowest Salary = $ 250

    Mean Salary = $ 900

    Median Salary = $800

    Range = $ 1000

    IQR = $ 700

    First Quartile = $ 450

    Standard Deviation = $ 400

    Part a)

    The following rule is used to identify Normal and Skewed distributions:

    For Normal Distribution, Mean is equal to Median For Left Skewed Distribution, Mean is lesser than Median For Right Skewed Distribution, Mean is greater than Median

    For the given case the value of Mean ($900) is greater than the Median ($800).

    Therefore, based on the given data we can conclude that:

    The distribution is skewed to the right because the mean is greater than the median.

    Part b)

    Middle 50% of the values lie between the First Quartile and the Third Quartile.

    The difference between First Quartile and Third Quartile is Inter-Quartile Range i. e. IQR

    IQR = Third Quartile - First Quartile

    Using Values in this equation gives us:

    700 = Third Quartile - 450

    Third Quartile = 1150

    This means, the middle 50% of the values lie between $ 450 and $ 1150
Know the Answer?