Calculating the Trimmed Mean

To find the trimmed mean of the given data set after removing one lowest and one highest value, we need to follow a series of steps.

Step 1: Understand the Data Set

The original data set is as follows:

2, 4, 4, 4, 5, 5, 7, 9

Step 2: Remove One Lowest and One Highest Value

1. Identify the lowest value: In the data set, the lowest value is 2.
2. Identify the highest value: The highest value is 9.

After removing these values, we are left with the following data set:

4, 4, 4, 5, 5, 7

Step 3: Calculate the Mean of the Remaining Data

Step 3.1: Sum the Remaining Values

Now, let's calculate the sum of the remaining values:

• (4 + 4 + 4 + 5 + 5 + 7 = 29)

Step 3.2: Count the Remaining Values

There are 6 values remaining in the data set.

Step 3.3: Calculate the Mean

The mean (average) is calculated by dividing the sum of the remaining values by the count of those values.

[ \text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{29}{6} \approx 4.8333 ]

This can be rounded to two decimal places:

• Mean ≈ 4.83

Final Results

Upon analyzing the options provided:

• A. 5.0
• B. 4.83
• C. 4.86
• D. 5.5

The calculated trimmed mean is approximately 4.83, which corresponds to option B.

Conclusion

Thus, the trimmed mean of the data set after removing one lowest and one highest value is:

B. 4.83