When a data set has an outlier which measure of center best describes the distribution?
Common Measures of CenterMean Show
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. 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. Procedure for finding
Formula What measure of center is best for outliers?The median is the most informative measure of central tendency for skewed distributions or distributions with outliers.
Which measure of the center of a distribution is most affected by an outlier?Mean is the only measure of central tendency that is always affected by an outlier. Mean, the average, is the most popular measure of central tendency. Calculator error when finding the mean: Students often forget to use parenthesis when finding the mean of a data set.
When outliers are present in the data set which measure is the best to describe central tendency in the data group of answer choices?Of the three measures of tendency, the mean is most heavily influenced by any outliers or skewness. In a symmetrical distribution, the mean, median, and mode are all equal. In these cases, the mean is often the preferred measure of central tendency.
Which is the best measure of center for this distribution?The mean and the median can be calculated to help you find the “center” of a data set. The mean is the best estimate for the actual data set, but the median is the best measurement when a data set contains several outliers or extreme values.
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