Mathematics

Question

When would you want to use the median over the mean for describing the measure of center for a data set??

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2 Answer

  • The median is the middlemost number of a data set, while the mean is the average of the data set. The mean is the most common measure on central tendency but the mean has one main disadvantage: it is particularly susceptible to the influence of outliers. 

    Let’s say you run a customer satisfaction survey with a sample of 9 and rate their overall satisfaction scores on a scale of 1 to 10. You get an average of 5.22. You know that in general, you tend to retain customers with a score over 3, so you’re satisfied, because this indicates that you’re still above where you want to be. But then, suddenly, you lose 6 of those 9 customers. You go back to look at your data, and you find these scores:

    1, 3, 3, 3, 3, 5, 9, 10, 10

    The median of this group is a 3, indicating that at least half of your customers or more were unhappy. The scores became lopsided because of the unexpected 10’s, and you missed out on an important part of your data – the midpoint that indicated that as many as half of your customers or more were dissatisfied with your company. Let’s say you run a customer satisfaction survey with a sample of 9 and rate their overall satisfaction scores on a scale of 1 to 10. You get an average of 5.22. You know that in general, you tend to retain customers with a score over 3, so you’re satisfied, because this indicates that you’re still above where you want to be. But then, suddenly, you lose 6 of those 9 customers. You go back to look at your data, and you find these scores:

    1, 3, 3, 3, 3, 5, 9, 10, 10

    The median of this group is a 3, indicating that at least half of your customers or more were unhappy. The scores became lopsided because of the unexpected 10’s, and you missed out on an important part of your data – the midpoint that indicated that as many as half of your customers or more were dissatisfied with your company. Median can play a major role in things like income level research as well, because a few millionaires may make it look like the socio-economic status of your sample is higher than it really is. Whenever a graph falls on a normal distribution, using the mean is a good choice. But if your data has extreme scores (such as the difference between a millionaire and someone making 30,000 a year), you will need to look at median, because you’ll find a much more representative number for your sample.

  • You would want to use the median when you have outliers in your data set.

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