Let's go step by step to find the mean, median, and mode of the given MLB batting averages.

Step 1: Organize the Data

The given data set is: 0.302, 0.278, 0.321, 0.283, 0.311, 0.312, 0.320, 0.276, 0.275, 0.281, 0.305, 0.277, 0.308, 0.303, 0.322

Let's sort the data in ascending order:

0.275, 0.276, 0.277, 0.278, 0.281, 0.283, 0.302, 0.303, 0.305, 0.308, 0.311, 0.312, 0.320, 0.321, 0.322

Step 2: Find the Mean

To calculate the mean, we add all the values together and divide by the number of values.

$\text{Mean} = \frac{\sum \text{values}}{\text{Number of values}} = \frac{0.275 + 0.276 + 0.277 + 0.278 + 0.281 + 0.283 + 0.302 + 0.303 + 0.305 + 0.308 + 0.311 + 0.312 + 0.320 + 0.321 + 0.322}{15}$

$\text{Mean} = \frac{4.619}{15} = 0.3079$

So, the mean is 0.308 (rounded to 3 decimal places).

Step 3: Find the Median

The median is the middle value of the sorted data set. Since there are 15 numbers (odd), the median will be the 8th value.

The sorted data set is: 0.275, 0.276, 0.277, 0.278, 0.281, 0.283, 0.302, 0.303, 0.305, 0.308, 0.311, 0.312, 0.320, 0.321, 0.322

The 8th value is 0.303, so the median is 0.303.

Step 4: Find the Mode

The mode is the value that appears most frequently in the data set. In this case, there are no repeating values, so the data set has no mode.

Final Answers:

• Mean: 0.308
• Median: 0.303
• Mode: No mode

Would you like a more detailed explanation of any of these steps? Here are some related questions to explore further:

1. How does the mean differ from the median and mode in skewed data?
2. What would happen if the dataset contained repeated values? How would that affect the mode?
3. Can the median be used as a better measure of central tendency than the mean in certain situations?
4. How do you calculate the standard deviation of a dataset like this one?
5. What is the significance of rounding numbers when calculating the mean, median, or mode?

Tip: The mode is particularly useful when analyzing categorical data, where numerical averages may not apply.