If the mean of 22, 25, 27, 24, and x is 26, then the value of x is:
32
Finding the Value of x Using the Mean
The question asks us to find the value of an unknown number, represented by 'x', given a set of numbers and their mean. The numbers are 22, 25, 27, 24, and x. The mean (average) of these five numbers is given as 26.
Understanding the Concept of Mean
The mean of a dataset is calculated by summing all the values in the dataset and then dividing by the total number of values. The formula for the mean is:
\( \text{Mean} = \frac{\sum \text{values}}{\text{Number of values}} \)
In this specific problem, we have 5 values: 22, 25, 27, 24, and x. The number of values is 5. The mean is given as 26.
Step-by-Step Calculation to Find x
- Sum the known values: First, let's add the known numbers together.
\( 22 + 25 + 27 + 24 = 98 \)
- Set up the mean equation: Now, we can use the formula for the mean, including the unknown value 'x'.
\( \text{Mean} = \frac{22 + 25 + 27 + 24 + x}{5} \)
We know the mean is 26, so the equation becomes:
\( 26 = \frac{98 + x}{5} \)
- Solve for x: To find the value of 'x', we need to isolate it in the equation.
- Multiply both sides of the equation by 5 to eliminate the denominator:
\( 26 \times 5 = 98 + x \)
\( 130 = 98 + x \)
- Subtract 98 from both sides of the equation to find 'x':
\( 130 - 98 = x \)
\( 32 = x \)
- Multiply both sides of the equation by 5 to eliminate the denominator:
Therefore, the value of x is 32.
Checking the Answer
We can check our answer by calculating the mean with x = 32:
\( \text{Mean} = \frac{22 + 25 + 27 + 24 + 32}{5} = \frac{130}{5} = 26 \)
This matches the given mean, confirming our calculation is correct.
Analysis of Options
Let's look at the given options:
- Option 1: 28
- Option 2: 41
- Option 3: 35
- Option 4: 32
Our calculated value for x is 32, which corresponds to Option 4.
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