8. For the date 4, 16, 20, 24, 38,57,59,60,60,74, compute the 10% trimmed mean.

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**Problem:** For the data 4, 16, 20, 24, 38, 57, 59, 60, 60, 74, compute the 10% trimmed mean.

**Solution Explanation:**

The 10% trimmed mean involves removing the top 10% and the bottom 10% of data points before calculating the mean. Here's how to compute it for the given data set:

1. **Order the data set:** Arrange the given numbers in ascending order.
   - Ordered data: 4, 16, 20, 24, 38, 57, 59, 60, 60, 74

2. **Determine the number of data points to trim:** With 10 data points:
   - Trim 10% of 10 = 1 data point from each end.

3. **Trim the data:** Remove the lowest and highest data points.
   - Trimmed data: 16, 20, 24, 38, 57, 59, 60, 60

4. **Calculate the mean of the trimmed data:**
   - Mean = (16 + 20 + 24 + 38 + 57 + 59 + 60 + 60) / 8
   - Mean = 334 / 8
   - Mean = 41.75

Thus, the 10% trimmed mean of the data set is 41.75.
Transcribed Image Text:**Problem:** For the data 4, 16, 20, 24, 38, 57, 59, 60, 60, 74, compute the 10% trimmed mean. **Solution Explanation:** The 10% trimmed mean involves removing the top 10% and the bottom 10% of data points before calculating the mean. Here's how to compute it for the given data set: 1. **Order the data set:** Arrange the given numbers in ascending order. - Ordered data: 4, 16, 20, 24, 38, 57, 59, 60, 60, 74 2. **Determine the number of data points to trim:** With 10 data points: - Trim 10% of 10 = 1 data point from each end. 3. **Trim the data:** Remove the lowest and highest data points. - Trimmed data: 16, 20, 24, 38, 57, 59, 60, 60 4. **Calculate the mean of the trimmed data:** - Mean = (16 + 20 + 24 + 38 + 57 + 59 + 60 + 60) / 8 - Mean = 334 / 8 - Mean = 41.75 Thus, the 10% trimmed mean of the data set is 41.75.
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