Let's calculate the required statistics step by step:

Data Set:

50, 49, 23, 12, 54, 37, 10, 29

Step 1: Mean

The mean is calculated as the sum of all data points divided by the number of data points.

$\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}$

$\text{Mean} = \frac{50 + 49 + 23 + 12 + 54 + 37 + 10 + 29}{8}$

$\text{Mean} = \frac{264}{8} = 33.0$

Step 2: Median

The median is the middle value when the data is arranged in ascending order. If there are an even number of data points, the median is the average of the two middle numbers.

1. Arrange data in ascending order: $10, 12, 23, 29, 37, 49, 50, 54$

2. Since there are 8 data points (even), the median is the average of the 4th and 5th numbers: $\text{Median} = \frac{29 + 37}{2} = 33.0$

Step 3: Mode

The mode is the number(s) that occur most frequently. If no number repeats, the mode does not exist (DNE).

• Observing the data: $10, 12, 23, 29, 37, 49, 50, 54$
• No number repeats.

$\text{Mode} = \text{DNE}$

Final Answer:

• Mean: 33.0
• Median: 33.0
• Mode: DNE

Would you like detailed steps or further clarifications?

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Related Questions:

1. How do you compute the range of the data set?
2. Can we calculate the variance and standard deviation of the data set?
3. How would the mean change if an additional data point is added?
4. What happens to the median if one of the numbers changes significantly?
5. Why is the mode sometimes not applicable in data sets?

Tip:

When calculating the median for large data sets, sorting the data accurately is critical to ensure the middle values are identified correctly.