Q 696. What does the skewness of a dataset indicate about its distribution? What are its different types and how do they affect the interpretation of statistical analyses?

 

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Skewness is a way to explain how the data is spread out around the mean. It tells us whether the data is more falling on one side or the other rather than being distributed equally

 

What does it indicate?

 

Direction of Tilt- Skewness reflects if the data is more towards the right , If yes then its is (Positive skewness) or it is towards left then its is (Negative Skewness)

 

Where is our mostly data - It shows where the most data points are positioned. If its is s case of Positive Skewness then data points are on the lower side. In negative Skewness- Data points are on the higher side

 

Outliers- Skewness can also suggest if there are unusual values or outliers that are far from the rest of the data

 

Types of Skewness

 

Positive Skewness (Right- Skewed)- Here the Mean is moreover larger than the median because the higher value pulls it up

Example= A batch of 20 candidates participated in Master black belt program . Most candidates scored  between 70% -80% out of 100 %, only some of them obtained  95% or more. The point here is that Mean score will be coming 85% due to the high scores but most students actually scored around 70 - 80 %, which makes the Mean higher than the typical for the batch . As a result of which we might think the class did good overall than they actually did

 

Negative Skewness (Left- Skewed)- Here mostly data points are on the higher side, however some low values pulls the average down.

Example- Think of a small company where mostly people are getting 20000 - 40000 INR salary, whoever is working from long back older is earning 10000 INR. The point here is that Mean salary will be coming around 25000 INR because of some old people getting 10000 INR salary. Even though the mostly people are getting 30000 INR salary. As a result of which mostly people will look getting less salary than the actually get.

 

Zero Skewness(- The distribution of datapoints is equally distributed)

Example when we play Ludo and imagine that the dice is giving 3,4,5,6 repetitively for number so times we played. In this case Mean will be 4.5 and mode will also be 4 or 5. The point here is that dataset will be evenly distributed actually each number has come about the same number of times

 

How it affects our Interpretation?

Skewness is crucial to understand for correct data interpretation ensuring that statistical analyses give valid and reliable result. It also represents that datasets are evenly spread or not that actually impacts the mean, mode and median and other measures

Skewness 

 

Skewness is a measure of asymmetry about mean for any distribution. In probability and statistics mathematics, any distribution is called asymmetrical if left hand and right-hand side of the distribution is not equal.  

 

Types of skewness

Skewness can be positive (on right side), Negative (on left hand side) or Zero (No skewness) about the mean. 

 

1. Positive Skewness: When a distribution has a longer tail on right hand side of it's peak, called positive skewness.
2. Negative Skewness: When  a distribution has a longer tail on left hand side of it's peak, called negative skewness.  
3. Zero Skewness: a distribution is symmetrical on both sides of mean and there is no skewness in data, it is called Zero skewness. 
4.  

 

 

 

Effect of skewness on data set interruption

 

As we see skewness shows that data is not equally distributed about mean. Data with skewness can affect in the following manners:-

• Skewness data can influence the accuracy of mean, median and mode calculations. 

• Outliers in skewed data can give wrong information about the data which can lead to wrong decisions. 

• Generative AI algorithm can give the wrong interpretation for predictive analytics if data is skewed and not taken care. 

 

By transforming the data for normal distribution, we can reduce skewness and provide higher reliability of statistical results. 

The best answer is provided by Puneet Vohra. Well done!

 

P.S. There were 10 answers posted, however, 8 of them could not be approved because they either failed the AI generated content or plagiarism tests