For the set (3, 4, 5, 8, x), the mean, the median and the mode all have the same value. What is the value of x?

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For the set (3, 4, 5, 8, x), the mean, the median and the mode all have the same value. What is the value of x?

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Answer 1 · 2017-04-01T05:32:33

5

Explanation:

Since there is only one mode, $x$ $x$ must be the mode and be either $3$ $3$ , $4$ $4$ , $5$ $5$ , or $8$ $8$ .

(If $x$ $x$ were not one of $3$ $3$ , $4$ $4$ , $5$ $5$ , or $8$ $8$ , then there will be no mode. Since it must be one of $3$ $3$ , $4$ $4$ , $5$ $5$ , or $8$ $8$ , $x$ $x$ will be the mode.)

But $x$ $x$ cannot be $3$ $3$ or $8$ $8$ . If it were either $3$ $3$ or $8$ $8$ , it would not be the median. But the median has the same value as the mode.

Thus, $x$ $x$ can only be $4$ $4$ or $5$ $5$ . Now, if you find the mean of the set when $x$ $x$ is $4$ $4$ , you get $\frac{3 + 4 + 5 + 8 + 4}{5} = \frac{24}{5}$ $(3+4+5+8+4)/5=24/5$ . If you find the mean of the set when $x$ $x$ is 5, you get $\frac{3 + 4 + 5 + 8 + 5}{5} = 5$ $(3+4+5+8+5)/5=5$ .

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For the set (3, 4, 5, 8, x), the mean, the median and the mode all have the same value. What is the value of x?

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