Which is more affected by extreme observations, the mean or median? And how about the standard deviation or IQR?mean, standard deviationmean, IQRmedian, standard deviationmedian, IQR
Question
Which is more affected by extreme observations, the mean or median? And how about the standard deviation or IQR?mean, standard deviationmean, IQRmedian, standard deviationmedian, IQR
Solution
The mean and standard deviation are more affected by extreme observations. This is because the mean is calculated by adding up all the numbers and then dividing by the total number of values, so a very high or very low value can significantly change the mean. Similarly, the standard deviation is a measure of the amount of variation or dispersion in a set of values, so an extreme value can significantly increase the standard deviation.
On the other hand, the median and IQR (Interquartile Range) are less affected by extreme observations. The median is the middle value in a data set, so it is not affected by high or low values. The IQR is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles, so it is also not affected by extreme values.
Similar Questions
2.Question 2The data shown above has one “extreme” observation relative to the others. In this case, which of the following is true? Select all that apply.1 pointThe Median of this data is a larger dollar amount than the Mean of this data.The Mean of this data is a larger dollar amount than the Median of this data.The Median more accurately reflects the typical data when the extreme observations are removed.The Mean more accurately reflects the typical data when the extreme observations are removed.
1. Which measure/s of central tendency is easily affected by an extreme score?*1 pointa. Mean and modeb. b. Meanc. c. Moded. d. Median
Which measure of central tendency is least affected by extreme values or outliers?
What is the primary merit of the median?It is based on all itemsIt is not affected by extreme valuesIt is suitable for interval dataIt is the most stable average
Which statement about the interquartile range is correct?Select one:a.Like the mean, the IQR is influenced by extreme values. So, it is not a useful measure of central tendency polygonb.Like the median, the IQR is not influenced by extreme values. So, it is another useful measure of central tendencyc.Like the mean, the IQR is not influenced by extreme values. So, it is another useful measure of central tendencyd.Like the median, the IQR is influenced by extreme values. So, it is not a useful measure of central tendency polygon
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