Central tendency

For each group, the mean income is higher than the median, indicating a positively skewed distribution where there are few extremely high values. When looking at individual groups, the largest difference between mean and median is within the white workers group; there is nearly a $21,000 ($20,651) difference, well above the other two groups as well as all workers.  Black workers see a difference of $15,026 between mean and median income and the difference among Latino workers is $16,700. I think white workers have the greatest absolute difference between mean and median because more white workers than black and Latino workers occupy high paying jobs, thus creating the largest difference among white workers.

In this case the mean is pulled in the direction of the extreme high incomes, creating an inflated mean income level. When interval-ratio variables are skewed such as this, it is best to choose either mode or median as the measure of central tendency.  For this reason, I would choose median as that is the measure of central tendency that represents the exact middle, alleviating the skewed effect of the extreme values on the high end.

 

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Examine figure below from the chapter’s “A Closer Look 4.2, A Cautionary Note: Representing Income.” Overall, how would you describe the differences between the median and mean incomes for each group? Why do you think white workers have the greatest absolute difference between median and mean incomes? If you had to report only one of these measures of central tendency, which one would you choose and why?

 

 

2 thoughts on “Central tendency

  • September 20, 2015 at 10:24 pm
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    Dear Sam,

    This is a great read. You have analyzed the data aptly and have written very well. I agree with you, I will also use median to analyze the central tendency for this particular case. I agree that when it is interval- ratio distribution such as this mode and median are the best ways to analyze central tendency. Although, it will not be advisable to use mode as a measure of central tendency in this case as it will mislead us by giving us highest value. I like the way you described everything including differences between mean and median incomes of each and every race.

    Rucha

  • September 20, 2015 at 7:41 pm
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    Your explanation of the data is very apt. I was kind of blown away by just how wide the gap between median and mean was!

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