Solution: Show
We know central measures include
Mean is the only measure of central tendency which depends on all the values as it is derived from the sum of the values divided by the number of observations. Median depends only on one or two middle most values. When the number of observations is odd, the median depends on the middle most value given by the value corresponding to (n+1)/2 term. Incase of even numbers, it depends on the average of two middle values given by (n + 1) / 2 and (n + 2) / 2 terms. Mode depends only on the values which are occurring for the maximum number of times. Thus, the mean will typically be strongly influenced by extreme values than the median. Therefore, the mean is the measure of central tendency most likely to be affected by an extreme value is true. True or False. The mean is the measure of central tendency most likely to be affected by an extreme value.Summary: The mean is the measure of central tendency most likely to be affected by an extreme value is true. Recommended textbook solutions
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Why is the mean most affected by outliers?An outlier can affect the mean by being unusually small or unusually large. In the previous example, Bill Gates had an unusually large income, which caused the mean to be misleading. The mean score is 84.6. However, if we remove the “0” score from the dataset, then the mean score becomes 94.
Which measure of central tendency is most affected by outliers in a skewed distribution?The preferred measure of central tendency often depends on the shape of the distribution. 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.
Which measure of the central tendency most affected and why?The mean is the measure of central tendency most likely to be affected by an extreme value. Mean is the only measure of central tendency which depends on all the values as it is derived from the sum of the values divided by the number of observations.
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Is the mean the measure of central tendency most likely to be affected by an outlier?
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