A third another statistic that has been proposed (in addition to the mean and median) to estimate the center of a dataset: the 5%-trimmed mean: throw out the bottom 2.5% and top 2.5% of the observations, then compute the sample mean of the remaining observations.
The mean is the most common measure of center. It is what most people think of when they hear the word "average". However, the mean is affected by extreme values so it may not be the best measure of center to use in a skewed distribution. Show Procedure for finding
Properties
Formula Median The median is the value in the center of the data. Half of the values are less than the median and half of the values are more than the median. It is probably the best measure of center to use in a skewed distribution. Procedure for finding
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Midrange The midrange is the midpoint between the lowest and highest values. Procedure for finding
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Formula Mode The mode is the most frequent value. If no value appears more than any other, then there is no mode. If two or more values appear more than the others, then the data is bimodal or multimodal. Procedure for finding
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Less Common Measures of CenterTrimmed Mean The trimmed mean is the mean after the lowest 10% of the values and the highest 10% of the values have been removed. The trimmed mean has the benefit over the regular mean that the extreme values have been cast out and so the trimmed mean is more resistant to change than the mean. Procedure for finding
Quadratic Mean The quadratic mean is used in some physical applications such as power distribution systems. It is also called the Root Mean Square (R.M.S.). Procedure for finding
Formula Geometric Mean The geometric mean only exists when all of the data values are positive. It is often used when finding the average of rates of change, rates of growth, or ratios. Procedure for finding
Formula Harmonic Mean The harmonic mean only exists when all of the values are positive. It is often used when the data consists of rates of change, such as speeds. Which is a characteristic of the mean as a measure of center?Answer and Explanation: One of the characteristics of the mean as a measure of centre is that "It is usually equal to the median in business data" as we do not have a lot of outliers.
What does the trimmed mean tell us?Key Takeaways
A trimmed mean removes a small designated percentage of the largest and smallest values before calculating the average. Using a trimmed mean helps eliminate the influence of outliers or data points on the tails that may unfairly affect the traditional mean.
What are the characteristics of trimmed mean that make it more valuable?The trimmed mean is calculated using a standard averaging method after the selected values have been removed. This method is very valuable because it helps correct any errors that would have occurred due to the presence of data points when determining the mean of a set of numbers or data.
Is trimmed mean a measure of central tendency?In contrast to the arithmetic mean , the trimmed mean is a robust measure of central tendency.
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