Which of the following describes a distribution with a long tail on one side, influencing the mean?

Which of the following describes a distribution with a long tail on one side, influencing the mean?

• A. Normal Distribution
• B. Bimodal Distribution
• C. Skewed Distribution
• D. Uniform Distribution

Answer: (C)

A distribution with a long tail on one side is known as a skewed distribution. This type of distribution is characterized by the presence of outliers or extreme values that significantly pull the mean toward the tail, resulting in a distortion of the typical central tendency. In a skewed distribution, if the tail extends towards the right, it's referred to as positively skewed, and if it extends to the left, it's called negatively skewed. The key aspect is that these tails lead to a situation where the mean, median, and mode are not all equal, contrasting with a normal distribution where they coincide. The mean is particularly sensitive to extreme values, making it a less reliable measure of central tendency in skewed distributions. Recognizing the implications of this is crucial for proper data analysis and interpretation. Specifically, in skewed distributions, reliance on the mean can obscure the reality of the data's central tendency and variability, aiding in making more informed decisions in research and program evaluation efforts.

A distribution with a long tail on one side is known as a skewed distribution. This type of distribution is characterized by the presence of outliers or extreme values that significantly pull the mean toward the tail, resulting in a distortion of the typical central tendency.

In a skewed distribution, if the tail extends towards the right, it's referred to as positively skewed, and if it extends to the left, it's called negatively skewed. The key aspect is that these tails lead to a situation where the mean, median, and mode are not all equal, contrasting with a normal distribution where they coincide. The mean is particularly sensitive to extreme values, making it a less reliable measure of central tendency in skewed distributions.

Recognizing the implications of this is crucial for proper data analysis and interpretation. Specifically, in skewed distributions, reliance on the mean can obscure the reality of the data's central tendency and variability, aiding in making more informed decisions in research and program evaluation efforts.