<h3>
Answer: Median = 4</h3>
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Explanation:
The mean is found by adding up all of the values and dividing by n, where n is the number of values in the set.
In this case, we have n = 7 values here. We count (x+1) as well since x is a placeholder for a number, which makes (x+1) also a placeholder in a sense.
As for what replaces x, we're not sure yet but we can use algebra to solve.
Lets add up all of the values given except for the "5" at the end. That 5 is the mean which is not part of the data set.
Adding up those values mentioned gives:
4+6+4+7+(x+1)+8+2 = x+32
Then divide this over n = 7 to get the mean 5
(x+32)/n = mean
(x+32)/7 = 5
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Let's isolate x
(x+32)/7 = 5
x+32 = 7*5
x+32 = 35
x = 35-32
x = 3
If x = 3, then x+1 = 3+1 = 4
So the (x+1) is being a placeholder for the number 4.
In other words, we'll replace the (x+1) with 4.
The data set of
4,6,4,7,(x+1),8,2
updates to
4,6,4,7,4,8,2
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We'll get to the median in a moment, but first we need to check if we have the correct replacement for (x+1)
Add up the values in the set {4,6,4,7,4,8,2}
Doing so leads to: 4+6+4+7+4+8+2 = 35
Then divide by n = 7 to compute the mean: 35/n = 35/7 = 5
We get the mean is 5 which matches with the instructions. So we have the correct replacement for the (x+1). We can now find the median.
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To find the median of any data set, we need to make sure the numbers are in order from smallest to largest.
Right now {4,6,4,7,4,8,2} is not sorted, but we can sort the items to get {2,4,4,4,6,7,8}
The median is at the exact middle. In this set, the median is that third copy of '4'. Note how "2,4,4" is to the left of the median while "6,7,8" is to the right of the median. There is the same number of values on either side of the median to show things are balanced and we are at the center point.
As an alternative, you can cross off each pair of outer values one at a time until you steadily arrive at the midpoint, which again is that third copy of '4'.
So that's why the median is 4.
