Right Skewed Histogram

 A right skewed histogram, or also known as a positively skewed histogram, is a type of data distribution where most of the data values are concentrated on the left side.

The tail extends to the right. This shows us that there are a few higher values that stretch out the distribution. In such a distribution, the mean is greater than the median due to influence of higher values.
 

Skewness refers to the asymmetry in the given data distribution. A symmetric distribution means that left and right sides mirror one another. Understanding the skewness of a distribution helps improve data interpretation and ensures accurate analysis.

In a left skewed distribution, the relationship between mean, median, and mode is mode > median > mean.

In a right skewed distribution, the relationship of mean, median, and mode is mean > median > mode. In symmetrical distributions, the relationship of mean, median, and mode is mean = median = mode. 

It is important to identify right skewed histogram because it helps in understanding data distribution among other prominent things. To identify a right skewed histogram, we use the following methods:

Calculate the Skewness: To find the skewness of a histogram, apply the formula: 

Skewness = (mean - median) / standard deviation.

To identify the right skewed histogram, we must check if the skewness is positive.

Visual Inspection: To identify the right skewed histogram, look for a longer tail on the right side than on the left side.

To interpret the histogram of right skewed data, you should have knowledge of the distribution as well as the impact of the skewness on the right side. These are the following points that are to be kept in mind when interpreting a right skewed histogram:

Data points always lies on the left side of the graph

The tail extends to the right side, stretching out.

If the dataset has very high values, the tail of the distribution is pulled toward the right side of the curve.

Data analysis is very dependent on the right skewed histogram, since this can render the data distribution with extreme values, and the shape of the data.

There are many differences between the right skewed and left skewed histogram. Some of them are mentioned in the table below:
 

Let us take the following example of a right skewed histogram to calculate the mean, median, and mode from the given dataset:
3, 3, 3, 6, 3, 9, 3, 3, 4, 8, 7, 6, 5, 4, 6, 7

Solution: 

Mean = 3 + 3 + 3 + 6 + 3 + 9 + 3 + 3 + 4 + 8 + 7 + 6 + 5 + 4 + 6 + 7 = 80
= 80/16 = 5.

Median: Arrange the data in ascending order:
3, 3, 3, 3, 3, 3, 4, 4, 5, 6, 6, 6, 7, 7, 8, 9.
Since there are 16 values, the 8th and 9th values are the middle values; so the average is taken 4+5/2 = 9/2 = 4.5.

Mode: the mode is the most frequently occurring value, in the data set given above the mode is 3. Because 3 is the most frequently occurring value.

Verification: In a right-skewed histogram, the relationship between the mean, median, and mode follows this pattern: Mean > Median > Mode. In the above example, the mean = 5, median = 4.5 and mode = 3. Hence, this proves that the above data is a right skewed histogram. 

Right skewed histograms have a lot of real world applications, some of them are given here:

Income and Wealth Distribution: We use right skewed histograms in income and wealth distribution to analyze the wealth gaps, it is also used to design progressive tax systems and to assess the impact of economic policies.

Sales and Revenue Data: We use right skewed histograms in sales and revenue data to identify the best-selling products, it is also used to plan the inventory and marketing strategies, and to forecast revenue growth.

Waiting Times and Service Durations: We use right skewed histograms in waiting times and service durations to optimize staffing schedules, to reduce customer wait times, and to improve service efficiency.