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
Properties
Midrange The midrange is the midpoint between the lowest and highest values. Procedure for finding
Properties
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
Properties
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 central tendency is resistant to extreme numbers?Right-skewed or Skewed Right
A right skewed distribution. Note! When one has very skewed data, it is better to use the median as measure of central tendency since the median is not much affected by extreme values.
Which measure is most resistant to extreme values?Median is the most resistant to variation in sampling because median is defined as the middle of ranked data so that 50% values are above it and 50% below it. As such, the extreme values are unable to affect median.
Which measure of central tendency is most affected by extreme values?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.
Which measure of center is resistant to extreme values in a data set?The median is not affected by outliers, therefore the MEDIAN IS A RESISTANT MEASURE OF CENTER.
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