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Let’s analyze and solve each part of this question based on the provided list of numbers:

The data given is:
\[ 123, 125, 137, 121, 137, 126 \]

### Step 1: Calculate the Mean (a)
The **mean** is calculated by adding all the numbers together and dividing by the number of values.

1. **Sum of values**:
   \[
   123 + 125 + 137 + 121 + 137 + 126 = 769
   \]

2. **Number of values**: 6

3. **Mean**:
   \[
   \text{Mean} = \frac{769}{6} \approx 128.2
   \]

So, the mean is approximately **128.2**.

### Step 2: Calculate the Median (b)
The **median** is the middle value when the numbers are arranged in ascending order. Since there is an even number of values, the median will be the average of the two middle numbers.

1. **Ordered data**: 
   \[
   121, 123, 125, 126, 137, 137
   \]

2. **Middle values**: 125 and 126

3. **Median**:
   \[
   \text{Median} = \frac{125 + 126}{2} = \frac{251}{2} = 125.5
   \]

So, the median is **125.5**.

### Step 3: Determine the Mode (c)
The **mode** is the number that appears most frequently in the list.

In this data set:
- **137** appears twice, while all other numbers appear only once.

Therefore, the mode is **137**.

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### Summary of Answers:
1. **Mean**: 128.2 (rounded to the nearest tenth)
2. **Median**: 125.5
3. **Mode**: 137

Since there is a mode, the answer for part (c) is option **A** with the mode being **137**.

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Would you like further details or have any questions on this solution?

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Here are some related questions to deepen your understanding:
1. How do you calculate the range of a data set?
2. How does adding a new data point affect the mean, median, and mode?
3. What happens to the median if there is an odd number of data points?
4. How would the mode change if two numbers had the same highest frequency?
5. Why is the median sometimes a better representation of central tendency than the mean?

**Tip**: For large data sets, arranging the data in ascending order before calculating median and mode can simplify your work.

For the following list of data, calculate (a) the mean, (b) the median, and (c) the mode or modes (if any):

123, 125, 137, 121, 137, 126

Learn how to calculate the mean, median, and mode of the data set 123, 125, 137, 121, 137, 126. This example illustrates the use of measures of central tendency, including calculating the mean by averaging, finding the median in an ordered list, and identifying the mode as the most frequent value.

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