Select the excel function for the 19 percent trimmed mean of a data set in cells A1:A100. How many observations would be trimmed in each tail?
The Correct Answer and Explanation is :
To calculate the 19 percent trimmed mean of a dataset in Excel for cells ranging from A1 to A100, you would use the TRIMMEAN function. The formula to use is:
=TRIMMEAN(A1:A100, 0.19)In this formula, 0.19 represents the total percentage of data points to trim from both tails of the dataset.
Explanation:
The TRIMMEAN function in Excel calculates the mean of a dataset after excluding a specified percentage of the smallest and largest values. The percentage value should be a decimal indicating the total proportion of the dataset to trim, not the amount per tail.
In the case of a 19% trimmed mean, 19% of the total observations from the dataset are excluded from the calculation of the mean. These trimmed observations are equally taken from both the lower and upper extremes of the data set.
For a dataset with 100 data points (as in cells A1:A100), trimming 19% implies that 19 observations in total are excluded. Since the trimming is symmetric, you would remove the lowest and highest 9.5% of the data points. However, since you cannot trim a half data point in practical terms, you would typically round to the nearest whole number. This rounding process might slightly adjust the exact percentage of data trimmed to fit whole numbers. Therefore, you would trim the lowest 10 and the highest 9 observations, or vice versa, depending on the rounding method applied. This results in a total of 19 observations being trimmed, with about 9 or 10 from each tail.
This approach to calculating a trimmed mean is useful for handling outliers or extremely varied data in your dataset, as it provides a more robust measure of central tendency than the arithmetic mean, which can be heavily influenced by extreme values.
Visual Aid:
I will generate an image that visually represents how the 19% trimmed mean would look on a dataset displayed as a line plot, highlighting the trimmed and included sections.
Let’s proceed with generating this visual explanation.
Here’s the visual representation of the 19 percent trimmed mean calculation on a dataset. This illustration shows how the data points are trimmed and included in the calculation, with the trimmed sections highlighted in red and the included data in green.
