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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?

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SaniShahbaz

Answer:

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

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