Find the 20%
trimmed mean of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

MLB Batting Averages
0.279
0.280
0.281
0.281
0.281
0.282
0.286
0.289
0.295
0.295
0.298
0.300
0.302
0.307
0.307
0.310
0.311
0.311
0.321
0.326

To find the 20% trimmed mean, follow these steps:

1. **Order the data** (already ordered in this case).
2. **Trim the data** by removing the lowest 20% and the highest 20% of the data.
3. **Calculate the mean** of the remaining data.

### Step 1: Determine the number of values to trim
- The data set has 20 values.
- 20% of 20 values is \( \frac{20 \times 0.20}{1} = 4 \) values.

So, we'll remove the lowest 4 and the highest 4 values.

### Step 2: Trim the data
Remove the lowest 4 values:
- 0.279, 0.280, 0.281, 0.281

Remove the highest 4 values:
- 0.311, 0.311, 0.321, 0.326

The remaining data after trimming is:
- 0.281, 0.282, 0.286, 0.289, 0.295, 0.295, 0.298, 0.300, 0.302, 0.307, 0.307, 0.310

### Step 3: Calculate the mean of the trimmed data
Add up the remaining values and divide by the number of values:

\[
\text{Sum} = 0.281 + 0.282 + 0.286 + 0.289 + 0.295 + 0.295 + 0.298 + 0.300 + 0.302 + 0.307 + 0.307 + 0.310 = 3.452
\]

\[
\text{Number of values} = 12
\]

\[
\text{Trimmed mean} = \frac{3.452}{12} \approx 0.2877
\]

### Final Answer:
The 20% trimmed mean is approximately **0.2877**.

Would you like further details or have any questions?

---

Here are 5 related questions you might explore:

1. How does trimming a different percentage of data affect the mean?
2. What are the advantages of using a trimmed mean over a regular mean?
3. How would you calculate the median of the same dataset?
4. Can you calculate the standard deviation of the trimmed data?
5. How does the trimmed mean compare to the overall mean of the original dataset?

**Tip:** Trimming data helps reduce the impact of outliers, giving a more robust central tendency measure.

Find the 20% trimmed mean of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

MLB Batting Averages
0.279
0.280
0.281
0.281
0.281
0.282
0.286
0.289
0.295
0.295
0.298
0.300
0.302
0.307
0.307
0.310
0.311
0.311
0.321
0.326

Discover how to calculate the 20% trimmed mean of a dataset with MLB batting averages. Follow a step-by-step solution, including how to trim the data and compute the mean, rounding to the appropriate decimal place. Suitable for high school students in Grades 9-12.

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