What is the value of x if 100,120,103,133,109,x have a mean of 110?

Question

Jason Olsen · Accepted Answer

Explanation:
This is a common statistics question.
Set up the equation so that
$\frac{100 + 120 + 103 + 133 + 109 + x}{6} = 110$
since you have 6 terms with an average of 110
$\frac{100 + 120 + 103 + 133 + 109 + x}{⧸ 6} \cdot ⧸ 6 = 110 \cdot 6$
100+120+103+133+109+x=660
Now subtract your know values to find x:
x=95

Jacob Trujillo · Accepted Answer

In order to solve this question, let us first give the formula to calculate the average of a set of numbers. Average or mean of a set of numbers is nothing but the sum of the numbers divided by the total number of terms in. The formula for mean can be given as,

\Rightarrow M e a n = \frac{x_{1} + x_{2} + \dots + x_{n}}{n}

Given the data as 100, 120, 103, 133, 109, x, we know the number of terms here is 6. We calculate the mean by substituting in the above formula.

\Rightarrow M e a n = \frac{100 + 120 + 103 + 133 + 109 + x}{6}

We also know the mean for the given data is already calculated as 110. Substituting this in the above equation too,

\Rightarrow 110 = \frac{100 + 120 + 103 + 133 + 109 + x}{6}

Multiplying both sides by 6 and adding all the terms in the numerator on the right-hand side,

\Rightarrow 110 \times 6 = 565 + x

Subtracting both sides by 565,

\Rightarrow 660 - 565 = 565 + x - 565

Subtracting the terms on the left-hand side, we get the value of x as,

\Rightarrow x = 95

What is the value of x if 100,120,103,133,109,x have a

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