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If the mean, median, and mode are all equal for the set (10, 80, 70, 120, x}, find the value of x.
X
(Simplify your answer. Type an integer or a decimal.)
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coolstick

Answer:

x=70

Step-by-step explanation:

First, we know that the mode is the number that is the most common. As each value in the set so far only has one of each number, we know that x must be one of the current numbers, making that the mode.

Next, because x is the mode and has to be the median as well, and our number line so far is

(10, 70, 80, 120), x must be either 70 or 80 to make it the median. This is because if x is 10 or 120, we would end up with (10, 10, 70, 80, 120) with 70 as the median or (10, 70, 80, 120, 120) with 80 as the median.

Finally, to calculate the mean, we have

mean = sum / count

The mean must be x, as it is equal to the mode, so we have

x = (10+70+80+120 + x)/5 (as there are 5 numbers including x)

multiply both sides by 5 to remove the denominator

5 * x = 10+70+80+120+x

5 * x = 280 + x

subtract x from both sides to isolate the x and the coefficient

4 * x = 280

divide both sides by 4 to get x

x= 70

We see that x is 70 or 80 and is one of the current numbers, checking off all boxes.

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