Right Skewed Histogram

A right-skewed histogram (also known as a Positively Skewed Distribution) is analogous to a lopsided hill. Instead of a perfect, symmetrical bell shape, the majority of the data is concentrated on the left side.

The defining feature of a skewed right histogram is the "tail." While the majority of the data is low, the tail extends comfortably to the right. This happens because a few unusually high values—the outliers—pull the distribution in that direction, resulting in the long, tapered shape.

Why does this happen? In a perfect world, data would be symmetric: the left side mirrors the right. However, real-world data frequently behaves differently. A right-skewed histogram tells the story of asymmetry.

Consider the salary structure of a large company. The majority of people earn entry-level or mid-level wages (the large hump on the left), but a few CEOs earn millions (the long tail on the right).

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

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.

• Check for Positivity: To identify the right skewed histogram, we must check if the skewness is positive.

• Visual Inspection: The tail on the right side is longer than the tail on the left side.

To interpret a histogram with right-skewed data, you need to understand the distribution and how the right-side skewness affects it. The following points are to be kept in mind when interpreting a right skewed histogram:

Data points always lie 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 dependent on the right skewed histogram, since this can render the data distribution with extreme values.

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

= \({80 \over 16}\) = 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 are the middle values; so the average is: \({{4 + 5} \over 2} = {9 \over 2} = 4.5\)

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. 

Understanding histograms can be tricky for children, especially when the data is not evenly spread. Right-skewed histograms have most values on the left and a long tail stretching to the right. 
 

• Most data values are on the left.
   
• Mean is greater than median, which is greater than mode.
   
• Remember: Right tail = Right skew.
   
• Compare with left-skewed and symmetric histograms.
   
• Look for extreme high values (outliers) on the right.
   
• Teach students that “Skew” describes the long, flat tail, not the big hump. If the tail points to the right, it is right-skewed.
   
• Remind them that the skew points to the side with fewer numbers (the outliers), not the side with the majority.
   
• Explain that the Mean is easily distracted. Like a billionaire walking into a room, high numbers on the right pull the Mean toward them. The Mean always “chases” the tail.
   
• Use examples like a difficult exam creates a Right Skew: most students score low (hump on the left), but a few geniuses score high (tail on the right).
   
• Have students physically stretch their right arm out to the side. If the graph looks like their right arm extending, it’s a Right Skew.
   
• Visualize sliding down the slope. The order as you go towards the tail is always Mode → Median → Mean (Mean is furthest right).

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 Time and Service Duration: We use right skewed histograms to optimize staffing schedules, reduce customers' wait time, and improve service efficiency.