How do outliers affect the mean, median, and mode of a data set?

In my experience as a data scientist, I've found the mean to be deceptively simple but tricky in practice, especially in income datasets similar to the example given. I remember a project where we analyzed regional sales data, and a few extraordinarily high transactions skewed our average significantly. This led us to initially overestimate the typical sales performance. To address this, we started using trimmed means, cutting off the top and bottom 5% of data, which gave a more realistic view of our central tendency.

Outliers have a significant impact on the mean, as they can skew it towards their extreme values. The median is less affected, as it's resistant to extreme values but may shift slightly if outliers are near the center. Outliers usually don't affect the mode, as it represents the most frequent values. Overall, outliers can distort the mean, minimally affect the median, and generally have no impact on the mode.

The mean, or average, is the sum of all data points divided by the number of points. Since it considers every value in the dataset, the mean is highly sensitive to outliers. A single outlier with an extreme value can significantly increase or decrease the mean.

Outliers have a substantial effect on the mean of a dataset. Since the mean is calculated by summing all values and dividing by the total number of observations, outliers can pull the mean towards their extreme values. A single outlier with an exceptionally high or low value can significantly distort the mean, making it less representative of the central tendency of the data.

Mean is nothing but the average of the categorical feature values if it is a numerical one. Since averages can be affected by a few very high positive numbers or negative numbers if present in the data. These rarely occurring numbers are known as outliers. So outliers can affect the mean severely if not handled. To deal with these type of problems we can first treat the feature values with outliers treatment methods, such as z-score treatment, quantile value treatment and remove them to calculate the mean which gives us the expected results.

The median, being the middle value of an ordered dataset, is resistant to outliers since it depends solely on the position rather than the value of the data points. This makes the median a more robust measure of central tendency when outliers are present. For instance, even with an extremely high salary outlier, the median salary remains within the range of the majority, offering a better representation of the central value.

The median is less sensitive to outliers compared to the mean. When calculating the median, the data is first sorted, and then the middle value (or the average of the two middle values for an even number of observations) is selected. Outliers have minimal impact on the median because they do not affect the position of the middle value in the sorted dataset. Therefore, the median provides a more robust measure of central tendency in the presence of outliers.

The median is the middle value when you line up all the values in order, and it's not as easily skewed by outliers as the mean is. In the context of fraud risk, if there are a few super high fraudulent transactions in your dataset, the median won't be thrown off as long as these outliers don't outnumber the normal transactions. For example, if most of a company's transactions are between ₹50 and ₹150, but there are a few fraudulent ones around ₹10,000, the median will still show the typical transaction value, giving a more accurate picture of normal behavior.

The mode is less sensitive to outliers than the median and mean. It means outliers have less effect on the mode. Outliers can affect the median but the mode remains stable. Robustness is measured by the rejection point which is the highest value that doesn't affect the measurement. The mode has a low rejection point while the median has an infinite one.

The mode, which is the most frequently occurring value in a dataset, is generally unaffected by outliers unless the outliers occur with high frequency. Outliers typically do not change the mode, making it a stable measure of central tendency. For example, if the most common salary in a dataset is $40,000, this mode remains unchanged even with the presence of an outlier like $1,000,000.

Outliers generally do not affect the mode of a dataset since the mode represents the most frequently occurring value(s) in the data. Outliers, which are by definition rare occurrences, typically do not influence the mode significantly. However, in some cases, if an outlier occurs frequently and forms its own distinct peak in the distribution, it may become a new mode.

The mode is the value that appears most often in a dataset and isn't usually affected by outliers unless those outliers show up a lot. In fraud detection, the mode can point out common transaction amounts. If fraudulent transactions are rare or unique, they won't change the mode. For instance, if most transactions are ₹100 and the fraudulent ones are around ₹10,000 but happen rarely, the mode will still be ₹100. This helps in identifying what typical transactions look like, making it easier to spot any unusual activity.

Outliers can cause skewness in the data distribution, with positive skew occurring when outliers are on the higher end and negative skew when they are on the lower end. This skewness affects the overall shape and symmetry of the data, complicating statistical analysis and the application of certain machine learning algorithms that assume a normal distribution. Skewed data might indicate a majority earning lower salaries with a few very high earners, influencing analysis outcomes and decision-making processes.

Outliers can skew the distribution of data towards their extreme values, leading to a non-normal distribution. In such cases, the mean may no longer be representative of the central tendency, as it is heavily influenced by the outliers. The median, being resistant to outliers, provides a better measure of the center of the distribution in skewed datasets.

Outliers can skew data, leading to a non-symmetrical distribution. In fraud risk, if the outliers are higher values, the data distribution can become right-skewed, showing more frequent lower transactions with occasional high values due to fraud. For example, if most transactions are under ₹200 but fraudulent ones are around ₹5,000, the distribution will have a long tail to the right. This skewness can complicate data analysis, making it tricky to detect fraud without using the right statistical methods to account for the skew.

Outliers can skew data, leading to a non-symmetrical distribution. In fraud risk, if outliers are high values, the data can become right-skewed, showing frequent low transactions with occasional high fraud ones. For example, if most transactions are under ₹200 but fraudulent ones are ₹5,000, the distribution will have a long tail to the right. This skewness complicates data analysis, making fraud detection tricky without proper statistical methods. Handling outliers involves identifying and deciding whether to remove or adjust them. For instance, a company might review any transaction above ₹2,000 manually to ensure genuine large transactions aren't mistaken for fraud and real fraud isn't missed.

It's essential to identify and handle outliers appropriately depending on the context of the analysis. Outliers can be treated by removing them, transforming the data, or using robust statistical measures that are less affected by outliers.

Robust measures of central tendency, such as trimmed mean or Winsorized mean, are less influenced by outliers compared to the traditional mean. These measures involve trimming or replacing extreme values with less extreme ones before calculating the mean, resulting in a more robust estimate of central tendency.