Math CentralQuandaries & Queries


Question from Ayssa, a student:

The median of the data set (24, 35, 30, 12, 40, x) is 28. What is the value of x?


To find the median of a data set you list the observations in numerical order and the median is either the middle observation if there are an odd number of observations, or the average of the middle two observations if there are an even number of observations. You have 6 observations in your data set and you know 5 of them. In order they are


Since the median is half way between the middle two observations the missing observation x, must be less than 28. If x is less than 28, and 28 is half way between x and 30, what is x?



Hint 1: To have a definite answer, you must be using the convention that the median of an even number of data is the mean of the two middle ones.

Hint 2: Can two of the five given numbers be the two middle data? Why?

Hint 3: if x is one of the two middle numbers what is the other?

So what is x?

Good Hunting!


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