If the median of the scores `1,2,x,4,5("where " 1 lt 2 lt x lt 4 lt 5)` is 3, then the mean of the scores is

Options

A. 2
B. 3
C. 4
D. 5

Answer

To solve the problem step by step, we need to find the value of \( x \) given that the median of the scores \( 1, 2, x, 4, 5 \) is 3, and then calculate the mean of these scores.

### Step 1: Understand the Median
The median of a set of numbers is the middle number when the numbers are arranged in ascending order. Since we have 5 numbers (which is odd), the median will be the third number in the ordered list.

### Step 2: Identify the Position of the Median
Given the numbers \( 1, 2, x, 4, 5 \) are already in ascending order (with the condition \( 1 < 2 < x < 4 < 5 \)), the third number is \( x \).

### Step 3: Set the Median Equal to 3
Since we are given that the median is 3, we can set up the equation:
\[ x = 3 \]

### Step 4: Substitute \( x \) Back into the List
Now that we know \( x = 3 \), we can substitute it back into the list of scores:
\[ 1, 2, 3, 4, 5 \]

### Step 5: Calculate the Mean
To find the mean, we need to calculate the sum of all the scores and then divide by the number of scores:
\[ \text{Sum} = 1 + 2 + 3 + 4 + 5 = 15 \]
The number of scores is 5, so the mean is:
\[ \text{Mean} = \frac{\text{Sum}}{\text{Number of Scores}} = \frac{15}{5} = 3 \]

### Final Answer
The mean of the scores is \( 3 \).

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