Right Skewed Histogram

Right-skewed histogram is a graph showing the distribution of the data that is skewed to the right end, which means the tail of the graph is around the right side. Interpreting this type of histogram is crucial because it helps understand data distribution. In a right-skewed histogram, the bulk of the data points are settled on the left side, whereas a few extreme values drag the tail on the right. In the following article, we will learn the concept of histograms with a more narrow focus on right-skewed histograms for normal distributions.

A histogram can be defined as a graphical presentation of the distribution pattern of the data. It has a bar chart that shows the frequency of data in the specific bins or the intersectional periods in a graphical format. The x-axis shows the values, and the y-axis illustrates the frequency or count of occurrences inside each interval. Histograms can detect different patterns, trends, and outliers in the gathered data.

A right-skewed histogram, also known as a positively skewed histogram, is a graphical representation of data whose distribution is skewed to the right. In a right-skewed histogram, most of the data points are concentrated on the left side of the histogram, with a few extending far to the right. In a right skewed histogram, the peak of the histogram lies left to the middle value.

Definition of Right-Skewed Histogram

A right-skewed histogram is a visual representation of the data whereby the tail of the histogram stretches towards the greater values, depicting that the skewness of the distribution toward the right side.

• Visual Inspection: Look for a longer tail on the right side than on the left side.
• Calculate Skewness: Apply the skewness formula: Skewness = (Mean – Median) /Standard Deviation. An asymmetrical distribution that skews right is indicated by a positive skewness value.
• Box Plot Analysis: A histogram plotting the relation will have a longer tail on the right part of the box.

Example: Consider a dataset of exam scores where most students scored between 60-80, but a few scored above 90. This distribution would exhibit a right-skewed histogram.

Interpreting a histogram of right-skewed data involves the knowledge of the data distribution as well as the impact of its skewness in favor of the right side. In a right-skewed histogram:

• Data points lie mainly on the left side of the graph; however, there is a long tail towards the right, stretching out.
• The fact that the histogram’s peak is found on the left means that smaller values occur more often compared to the remaining values in the data set.
• If the outliers (extreme values) are high to the distribution then they push the tail to the right of the curve.
• The mean value of a right-skewed distribution is higher than the median which is also higher than the mode.
• The lack of equality in the distribution of data is made obvious from the box plot whose line runs to the right. This may mean that there are a few high values which contribute greatly to the overall appearance of distribution.
• Data analysis is very dependent on being able to understand a right-skewed histogram since this can render the data distribution with outliers, and the total shape of the data.

• Mode: The mode, which is the most frequent value, appears at the highest point of the histogram. As in the case of a right-skewed distribution the mode is typically the smallest of the three measures of central tendency.
• Median: The median is the middle value when that data is arranged from the smallest to the largest. It divides the data into two parts. In a right skewed histogram the median shifts to a right position of the mode.
• Mean: The mean is the sum of all values divided by the total number of values. It is the arithmetic average and is influenced by extreme values. In a right-skewed distribution, the mean is the largest of the three measures and is pulled to the right by the long tail.

The relationship between mean, median, and mode in a right-skewed histogram can be summarized as:

• The mode is the smallest value, representing the peak of the distribution.
• The median is greater than the mode and falls to the right of the peak.
• The mean is the largest value, pulled to the right by the long tail of the distribution.

This relationship, where Mean ≥ Median ≥ Mode, is a key characteristic of a right-skewed histogram.

The mean, median mode in a right skewed histogram can be shown using the graph below.

Example: Calculate the mean, median, and mode in a right skewed histogram, let’s consider a simple example with the following dataset: 2, 3, 3, 4, 3, 8, 3, 3, 2, 5, 7, 4, 5, 4, 6.

Solution:

Mean Calculation:

Mean = (2 + 3 + 3 + 4 + 3 + 8 + 3 + 3 + 2 + 5 + 7 + 4 + 5 + 4 + 6) / 15

Mean = 60 / 15

Mean = 4

Median Calculation:

Arrange the data in ascending order: 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7, 8

Since there are 15 values, the median is the 8th value, which is 4.

Mode Calculation:

The mode is the most frequently occurring value in the dataset. In this case, the mode is 3, as it appears 5 times, which is more frequent than any other value.

Verification of Property:

In a right-skewed histogram, the property states that Mean ≥ Median ≥ Mode. Let’s verify this with the calculated values:

Mean = 4

Median = 4

Mode = 3

As per the calculation, Mean (4) is greater than or equal to Median (4), which is greater than Mode (3), confirming that in a right-skewed histogram, the Mean is greater than or equal to the Median, which is greater than the Mode.

The difference between right skewed and left skewed histogram are mentioned below:

The image of the right vs left skewed histogram is shown below:

In short, right-skewed histograms should be grasped very well for unbiased data distribution analysis. The statistics can be computed by finding, summing, and evaluating the mean, median, and mode, which will help discover the movement pattern from the background data. Knowing or differentiating the right-skewed or left-skewed histograms will enable the researchers and analysts to make informed decisions based on the distribution characteristics. Knowledge of histograms and skewness allows data analysis to be more accurate and makes research more reliable for different fields.

Also, Check

• Central Tendency
• Central Limit Theorem
• Bar Graph

What is a right-skewed histogram?

The distribution is called a right-skewed by the fact that the data is clustered to the left and the tail is stretched to the right side.

What does a right-skewed histogram indicate?

It suggests there are fewer data on the right side and more on the left, whose tail will be longer on the right side.

What is skewness?

Skewness measures the asymmetry of a distribution. Positive skewness means the tail is on the right side.

What are the properties of a right-skewed histogram?

The properties of a right-skewed histogram are; the tail on the right is longer, the mean here is more than the median, and the mode is less than the median.

Which distribution is always right skewed?

The exponential distribution is always right-skewed.