If the mode of `22 ,\ 21 ,\ 23 ,\ 24 ,\ 21 ,\ 20 ,\ 23 ,\ 26 ,\ x` and `26` is `23`, then `x=`

Options

A. 20
B. 21
C. 23
D. 24

Answer

To solve the problem, we need to find the value of \( x \) such that the mode of the numbers \( 22, 21, 23, 24, 21, 20, 23, 26, x, \) and \( 26 \) is \( 23 \).

### Step-by-Step Solution:

1. **List the Given Numbers**:
The numbers we have are \( 22, 21, 23, 24, 21, 20, 23, 26, x, 26 \).

2. **Count the Frequency of Each Number**:
- \( 20 \): 1 time
- \( 21 \): 2 times
- \( 22 \): 1 time
- \( 23 \): 2 times
- \( 24 \): 1 time
- \( 26 \): 2 times
- \( x \): 1 time (unknown)

3. **Identify the Mode**:
The mode is the number that appears most frequently. Currently, \( 21, 23, \) and \( 26 \) each appear 2 times.

4. **Determine the Condition for Mode to be 23**:
For \( 23 \) to be the mode, it must appear more frequently than any other number. This means \( 23 \) must occur at least 3 times.

5. **Calculate the Required Occurrences of 23**:
Since \( 23 \) already appears 2 times, we need to make it appear one more time by setting \( x = 23 \).

6. **Substitute \( x \) with 23**:
If we set \( x = 23 \), the new frequency of \( 23 \) becomes 3 times:
- \( 20 \): 1 time
- \( 21 \): 2 times
- \( 22 \): 1 time
- \( 23 \): 3 times (after adding \( x \))
- \( 24 \): 1 time
- \( 26 \): 2 times

7. **Conclusion**:
Now, \( 23 \) appears 3 times, which is more than any other number. Therefore, the mode is indeed \( 23 \).

Thus, the value of \( x \) is \( 23 \).

### Final Answer:
\( x = 23 \)