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Mathematics Problem of the Week


> Home > MPOTW > 12/07/2022

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Can you list the numbers?

A list of twelve numbers have a range of eight, a mean, median & mode of five, if you picked one at random you had a fifty percent chance of a prime number, & there are as many even numbers as odd. List all twelve members.

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Solution to follow …

We have twelve numbers, so n=12 & the mean is x-=Σxi12=5 Σxi =60 The median is five too but as there are an even number of elements the mode is the mean of the sixth & seventh element when listed in order, so median = x6+x7 2 =5 x6 + x7 =10 Furthermore, the mode is also five ??? The range is eight, so x max - x min = 8 If the numbers are ordered this becomes x 12 - x 1 = 8 The mode is five, so there are at least two fives in the set.
Knowing the P(X=prime) = 0.5 so there must be six prime numbers (some are repeated, eg. five)

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