Question
What is the missing number in a set of numbers 10.2, 11.5, 9.8 and 12.1 when the average is 11?
Answers
Answered by
GPT-4o mini
To find the missing number, we can use the formula for the average.
The average of a set of numbers is given by:
\[
\text{Average} = \frac{\text{Sum of all numbers}}{\text{Count of numbers}}
\]
In this case, we have the numbers 10.2, 11.5, 9.8, and 12.1, plus the missing number \( x \). The count of numbers will be 5, since there are four known numbers and one unknown.
The average is stated to be 11, so we can set up the equation:
\[
11 = \frac{10.2 + 11.5 + 9.8 + 12.1 + x}{5}
\]
Now, let's first calculate the sum of the known numbers:
\[
10.2 + 11.5 + 9.8 + 12.1 = 43.6
\]
Now substituting this sum into our equation:
\[
11 = \frac{43.6 + x}{5}
\]
Next, we multiply both sides of the equation by 5 to eliminate the denominator:
\[
55 = 43.6 + x
\]
Now, we can solve for \( x \):
\[
x = 55 - 43.6
\]
\[
x = 11.4
\]
Therefore, the missing number is **11.4**.
The average of a set of numbers is given by:
\[
\text{Average} = \frac{\text{Sum of all numbers}}{\text{Count of numbers}}
\]
In this case, we have the numbers 10.2, 11.5, 9.8, and 12.1, plus the missing number \( x \). The count of numbers will be 5, since there are four known numbers and one unknown.
The average is stated to be 11, so we can set up the equation:
\[
11 = \frac{10.2 + 11.5 + 9.8 + 12.1 + x}{5}
\]
Now, let's first calculate the sum of the known numbers:
\[
10.2 + 11.5 + 9.8 + 12.1 = 43.6
\]
Now substituting this sum into our equation:
\[
11 = \frac{43.6 + x}{5}
\]
Next, we multiply both sides of the equation by 5 to eliminate the denominator:
\[
55 = 43.6 + x
\]
Now, we can solve for \( x \):
\[
x = 55 - 43.6
\]
\[
x = 11.4
\]
Therefore, the missing number is **11.4**.