Question

The mean of the scores 12, 15, \[x\], 19, 25, 44 is 25. Then \[x = \_\_\_\_\].
A) 20
B) 25
C) 30
D) 35

Answer 1

Hint:
Here, we will use the formula to calculate the mean is by dividing the sum of the terms by the number of the terms, that is, \[{\text{Mean}} = \dfrac{{{\text{Sum of the terms}}}}{{{\text{Number of terms}}}}\]. Then we will substitute the given numbers and total number of terms in the formula of mean to find the required value.

Complete step by step solution:
It is given that the mean of the scores 12, 15, \[x\], 19, 25, 44 is 25.
We know that the formula to calculate the mean is by dividing the sum of the terms by the number of the terms, that is, \[{\text{Mean}} = \dfrac{{{\text{Sum of the terms}}}}{{{\text{Number of terms}}}}\].
We will now find the sum of the given terms 12, 15, \[x\], 19, 25, 44.
\[12 + 15 + x + 19 + 25 + 44 = 115 + x\]
Now we will find the total number of terms.
6
Substituting the above values of the sum of the given numbers and total number of terms in the formula of mean, we get
\[{\text{Mean}} = \dfrac{{115 + x}}{6}\]
Since we know that the mean of the given numbers is 25.
Replacing 25 for Mean in the above equation, we get
\[25 = \dfrac{{115 + x}}{6}\]
Multiplying the above equation by 6 on each of the sides, we get
\[
   \Rightarrow 25 \times 6 = 6\left( {\dfrac{{115 + x}}{6}} \right) \\
   \Rightarrow 150 = 115 + x \\
 \]
Subtracting the above equation by 115 on each of the sides, we get
\[
   \Rightarrow 150 - 115 = 115 + x - 115 \\
   \Rightarrow 35 = x \\
   \Rightarrow x = 35 \\
 \]
Therefore, the value of \[x\] is 35.

Hence, option D is correct.

Note:
The value depends on the list of the numbers, the data may vary, so while solving these types of questions, you should be familiar with the formula to calculate the mean. Students should know that the arithmetic mean of a list of numbers is the sum of all the numbers divided by the amount of numbers. Then this question is really simple to find the value of \[x\].