Median, mode, quartiles, quintiles and so on, except when you get to very large number of percentiles.
The mean is most affected. Mode and Median are not influenced as much by outliers.
there are no limits to outliers there are no limits to outliers
The median is least affected by an extreme outlier. Mean and standard deviation ARE affected by extreme outliers.
The box and whisker plot informs you of the 5 number summary, which comprises of the minimum and maximum, the median, and the first and third quartiles. The minumum and maximum give you the range, which is not given by measures of central tendancy. also, if it a modified box and whisker plot, outliers will be marked separatley from the rest of the plot, outliers are also not included in the measures of center.
The sample range could be used as an index of dispersion. However, there are objections. One is that this statistic is obviously sensitive to outliers. Another is that for many population distributions there are measures with much better characteristics, even ignoring the problem of outliers.
The mean is most affected. Mode and Median are not influenced as much by outliers.
The mean is the measure of central tendency most influenced by outliers. Since it is calculated by summing all values and dividing by the number of values, extreme values can significantly skew the result. In contrast, the median and mode are less affected by outliers, making them more robust measures in such situations.
the mean is affected by outliers
Yes.
Extreme outliers can greatly distort statistical measures such as the mean and standard deviation, making them less representative of the data. They can also impact the accuracy of predictive models by leading to overfitting. In some cases, outliers may signal data quality issues or the presence of unexpected patterns in the data that warrant further investigation.
Outliers can significantly skew measures of center, such as the mean, by pulling the average in their direction, which may not represent the overall data well. For instance, a single extremely high or low value can distort the mean, making it less reflective of the typical values in the dataset. In contrast, the median is more robust against outliers, as it focuses on the middle value, thus providing a more accurate measure of central tendency in such cases. Overall, the presence of outliers necessitates careful consideration when interpreting measures of center.
there are no limits to outliers there are no limits to outliers
Yes, the mean is generally a better measure of central tendency when there are no outliers, as it takes into account all values in the dataset and provides a mathematically precise average. In the absence of outliers, the mean reflects the true center of the data distribution effectively. However, in the presence of outliers, the median might be preferred since it is less affected by extreme values.
The median is least affected by an extreme outlier. Mean and standard deviation ARE affected by extreme outliers.
The box and whisker plot informs you of the 5 number summary, which comprises of the minimum and maximum, the median, and the first and third quartiles. The minumum and maximum give you the range, which is not given by measures of central tendancy. also, if it a modified box and whisker plot, outliers will be marked separatley from the rest of the plot, outliers are also not included in the measures of center.
The sample range could be used as an index of dispersion. However, there are objections. One is that this statistic is obviously sensitive to outliers. Another is that for many population distributions there are measures with much better characteristics, even ignoring the problem of outliers.
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