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Chapter 3: Problem 6

Is it possible for a (quantitative) data set to have no mean, no median, or no mode? Give an example of a data set for which this summary measure does not exist.

Short Answer

Expert verified
In most quantitative data sets, we can calculate the measures of mean, median and mode. An exception to this is a data set with all unique values, where we cannot determine a mode since no value repeats. Also, an empty data set doesn't have a mean, median, or mode.

Step by step solution

01

Understanding Mean, Median, Mode

In statistical language, the mean is the average, calculated by adding all numbers in a data set and dividing by the amount of numbers in the set. The median is the mid-point value in a data set when the values are arranged in order, while Mode is the number which occurs most frequently in a data set.
02

Example for No Mode

Consider the data set: \[ \] {1, 2, 3, 4, 5}. Every number in this set appears once, so there isn't a mode here since no number appears more than once. This set, however, clearly has a mean (3) and median (3).
03

Example for No Mean and No Median

If you have an empty set, there will be no mean or median, as there are no values to calculate these summary measures. Obviously, there will be no mode for an empty set as well.

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Most popular questions from this chapter

Briefly describe how the percentiles are calculated for a data set.

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