Normal Distribution vs. Positively Skewed Distribution

Attribute	Normal Distribution	Positively Skewed Distribution
Shape	Symmetric bell-shaped curve	Skewed to the right
Mean, Median, Mode	Equal	Mean > Median > Mode
Tails	Equal tails on both sides	Longer tail on the right side
Central Tendency	Centered around the mean	Mean pulled towards the tail
Skewness	Skewness = 0	Skewness > 0

Introduction

Normal distribution and positively skewed distribution are two common types of probability distributions used in statistics. Understanding the attributes of these distributions is essential for analyzing data and making informed decisions. In this article, we will compare the characteristics of normal distribution and positively skewed distribution to highlight their differences and similarities.

Normal Distribution

Normal distribution, also known as the Gaussian distribution, is a bell-shaped symmetrical distribution where the mean, median, and mode are all equal. In a normal distribution, the data is evenly distributed around the mean, with approximately 68% of the data falling within one standard deviation of the mean, 95% falling within two standard deviations, and 99.7% falling within three standard deviations. The shape of a normal distribution is defined by its mean and standard deviation, with the curve being symmetrical around the mean.

One of the key characteristics of a normal distribution is that it is unimodal, meaning it has only one peak. This makes it easy to interpret and analyze data using the properties of the normal distribution. Normal distributions are commonly used in various fields such as finance, biology, and psychology due to their predictable and well-understood properties.

Another important attribute of a normal distribution is that it is defined by its mean and standard deviation. The mean represents the central tendency of the data, while the standard deviation measures the spread of the data around the mean. These parameters allow us to make inferences about the data and calculate probabilities for different outcomes.

Normal distribution is often used as a benchmark for comparing other distributions due to its well-known properties and widespread applicability. It is a fundamental concept in statistics and serves as the basis for many statistical tests and models.

In summary, normal distribution is a symmetrical bell-shaped distribution with a single peak, defined by its mean and standard deviation. It is widely used in various fields and serves as a benchmark for comparing other distributions.

Positively Skewed Distribution

Positively skewed distribution, also known as right-skewed distribution, is a type of distribution where the tail of the distribution extends to the right, indicating that the data is concentrated on the left side of the distribution. In a positively skewed distribution, the mean is typically greater than the median and mode, as the skewness is towards the higher end of the data.

One of the key characteristics of a positively skewed distribution is that it is unimodal, meaning it has only one peak. However, the peak is shifted towards the lower end of the data, with a long tail extending to the right. This asymmetry in the distribution can affect the interpretation of the data and the calculations of central tendency.

Positively skewed distributions are common in real-world data, especially in scenarios where there is a natural limit on the lower end of the data. For example, income distribution is often positively skewed, as there is a minimum income level below which individuals cannot earn. This results in a concentration of data on the lower end, leading to a positively skewed distribution.

Another important attribute of a positively skewed distribution is that it can affect the interpretation of statistical measures such as the mean and standard deviation. Since the mean is influenced by extreme values in the tail of the distribution, it may not accurately represent the central tendency of the data. In such cases, the median is often used as a more robust measure of central tendency.

Positively skewed distributions are commonly encountered in various fields such as finance, economics, and biology. Understanding the properties of positively skewed distributions is essential for analyzing data and making accurate predictions based on the underlying distribution.

In summary, positively skewed distribution is an asymmetrical distribution with a long tail extending to the right, indicating a concentration of data on the lower end. It is commonly encountered in real-world data and can affect the interpretation of central tendency measures.

Comparison

While normal distribution and positively skewed distribution have some similarities, such as being unimodal and having a single peak, they also have several key differences that distinguish them from each other. One of the main differences is the symmetry of the distribution - normal distribution is symmetrical, while positively skewed distribution is asymmetrical.

Another difference between the two distributions is the location of the peak relative to the mean. In a normal distribution, the peak is centered around the mean, while in a positively skewed distribution, the peak is shifted towards the lower end of the data. This difference in peak location can affect the interpretation of the data and the calculation of central tendency measures.

Furthermore, the tail of the distribution in a normal distribution is balanced on both sides of the mean, while in a positively skewed distribution, the tail extends to the right, indicating a concentration of data on the lower end. This asymmetry in the tail of the distribution can impact the analysis and interpretation of the data.

Additionally, the mean, median, and mode of a normal distribution are all equal, while in a positively skewed distribution, the mean is typically greater than the median and mode. This difference in central tendency measures reflects the skewness of the distribution and can influence the choice of statistical measures used for analysis.

Overall, while normal distribution and positively skewed distribution share some similarities, such as being unimodal, they also have distinct differences in terms of symmetry, peak location, tail shape, and central tendency measures. Understanding these differences is essential for accurately analyzing data and making informed decisions based on the underlying distribution.