In a list of 4 numbers, we know the mean is 54, the mean of the middle two values is 56, and the mode is 60. What is the mean of the smallest and largest numbers?

1 Answer
MathFact-orials.blogspot.com
Aug 8, 2017

52

Explanation:

#bb("mean")="sum of values"/"count of values"#

#54="sum of values"/4#

#"sum of values"=216#

~~~~~

#bb("median with an even number of values")="mean of the two middle values"#

#"mean of the two middle values"=56="sum of middle values"/2#

#"sum of middle values"=112#

#:. "sum of largest and smallest values"=216-112=104#

#:. bb("mean of largest and smallest numbers")=104/2=52#

~~~~~

We can also approach this problem using the mode:

#bb("mode")="value that appears most often"#

In this list of four values, let's set the two largest as 60 (with the mean and median being less than 60, we can safely say that the most listed number is also the biggest. We can also safely say, given that the median and mean are different, that the 60 is listed twice and not three or more times). This gives then:

Smallest value# = 104-60=44#

Next biggest value# = 112-60=52#

The two biggest values# =60#

#:. bb("mean of largest and smallest numbers")=(44+60)/2=52#

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