What is Positively Skewed Distribution?

Example

Income distributes positively if more population falls in the normal or lower-income earning group rather than a few high-earning income groups. In addition, they show the mean is greater than the median.

Below are the data taken from the sample. In the first column, given the income category. And in the second column, the number of persons falling in the respective income group is given. Next, calculate the meanMeanMean refers to the mathematical average calculated for two or more values. There are primarily two ways: arithmetic mean, where all the numbers are added and divided by their weight, and in geometric mean, we multiply the numbers together, take the Nth root and subtract it with one.read more, medianMedianThe median formula in statistics is used to determine the middle number in a data set that is arranged in ascending order. Median ={(n+1)/2}thread more, and mode and analyze whether it is an example of a positively skewed distribution.

Solution:

Calculation of the mean, median and mode:

#1 – Mean:

Mean of the data is:

  • Mean = (2,000 + 4,000 + 6,000 + 5,000 + 3,000 + 1,000 + 1,500 + 500 + 100 +150) / 10Mean = 2,325

#2 – Median:

  • Median Value =(10 + 1 / 2) th valueMedian Value = 5.5 th value i.e. average of 5th and 6th valueMedian = (3,000 + 1,000) / 2Median = 2,000

#3 – Mode:

The mode will be the highest value in the data set, which is 6,000 in the present case.

Analysis:

Here,

  • Mean > Median2325 > 2000

The mean is greater than the median in positively distributed data, and most people fall on the lower side. The same is the case n the above example.

What Causes Positively Skewed Distribution?

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#1 – Inequality in Distribution

The amount of money earned by everyone will differ. Earning depends upon working capacity, opportunities, and other factors. Similarly, the probability of any outcome is different. Hence, the main cause of positively skewed distribution is unequal distribution.

#2 – Homogenous Groups

The positive distribution reflects the same line of groups. That is, there is a more or less homogenous kind of outcome like in the case of the positive income distribution, the population in the lower or middle earning groups, i.e., the earning is more or less homogenous.

#3 – Desirable Returns

In finance, if the returns are desirable, they are said to be positively distributed. In positive distribution, the chances of profits are more than the loss.

#4 – Predictive Approach

The predictive approach towards data distribution into groups also causes such a distribution.

Positively Skewed Distribution Mean and Median

In a positively skewed distribution, the mean is greater than the median as the data is more towards the lower side and the mean average of all the values. In contrast, the median is the middle value of the data. So, if the data is more bent towards the lower side, the average will be more than the middle value. Let’s take the following example for better understanding:

  • 50, 51, 52, 59 shows the distribution is positively skewed as data is normally or positively scattered range.The mean of the data provided is 53 (average, i.e., (50+51+52+59)/4).Median is (n+1/2) Value, i.e. (4+1/2), i.e., 2.5, i.e., the median is average of 2nd value and 3rd value.Median is (51+52)/2 = 51.5As the mean is 53 and the median is 51.5, the data is said to be positively skewed.

Central Tendency in Positively Skewed Distribution

Central TendencyCentral TendencyCentral Tendency is a statistical measure that displays the centre point of the entire Data Distribution & you can find it using 3 different measures, i.e., Mean, Median, & Mode.read more is the mean, median, and mode of the distribution. The mean, median, and mode are equal in the normal skewed distribution data. Whereas the central tendency of positively skewed data has the following equation:

The mean is average, the median is the middle value, and the mode is the highest value in the data distribution. Therefore, the results bent towards the lower side as in this data type. Hence, the mean will be more than the median as the median is the middle value, and the mode is always the highest value. Therefore, any Skewed DistributionSkewness is the deviation or degree of asymmetry shown by a bell curve or the normal distribution within a given data set. If the curve shifts to the right, it is considered positive skewness, while a curve shifted to the left represents negative skewness.read more is always greater than the mean and median.

Conclusion

It is the type of distribution where the data is more toward the lower side. That means there are more or less homogenous types of groups. In a positively skewed distribution, most values on the graph are on the left side, and the curve is longer towards the right trail. In this distribution, the mean is greater than the median. In finance, it is the chance for more profits than the loss. In the case of income distribution, if most population earns in the lower and middle range, then the income is said to be positively distributed. Uneven distribution is the main cause for determining the positive or negative distribution.

This article has been a guide to what is Positively Skewed Distribution and its definition. Here, we discuss a positively skewed distribution with causes and graphs. You may also have a look at the following articles: –

  • Negatively Skewed DistributionCentral Limit Theorem.Standard Error FormulaArithmetic MeanGeometric Mean