For the set (3, 4, 5, 8, x), the mean,

Kiana Dodson

Kiana Dodson

Answered question

2022-06-21

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?

Answer & Explanation

upornompe

upornompe

Beginner2022-06-22Added 20 answers

Since there is only one mode, x must be the mode and be either 3,4,5, or 8.
(If x were not one of 3,4,5, or 8, then there will be no mode. Since it must be one of 3,4,5, or 8, x will be the mode.)
But x cannot be 3 or 8. If it were either 3 or 8, it would not be the median. But the median has the same value as the mode.
Thus, x can only be 4 or 5. Now, if you find the mean of the set when x is 4, you get
3 + 4 + 5 + 8 + 4 5 = 24 5 . If you find the mean of the set when x is 5, you get
3 + 4 + 5 + 8 + 5 5 = 5.

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