Can Normal Distribution Be Skewed: Detailed Facts, Examples And FAQs


Normal distribution is skewed with zero skewness, so the answer to the most common confusion can normal distribution be skewed is normal distribution is not skewed distribution as the curve of the normal distribution is symmetric without tail whose skewness is zero. The normal distribution curve is bell shaped with symmetry on the curve.

Since the skewness is lack of symmetry in the curve so if the symmetry is present in the curve there is lack of skewness.

How do you tell if the data is normally distributed?

For the data to check whether normally distributed or not just try to sketch the histogram and from the curve of the curve if the symmetry is present in the curve then the data is normally distributed, from the curve of data itself the question can normal distribution be skewed or not cleared if the concept of skewness is clear. Sketching the histogram or curve in each case is tedious or time consuming so instead of that their are number of statistical tests like Anderson-Darling statistic (AD) which are more useful to tell whether data is normally distributed or not.

The data which follows normal distribution have zero skewness in the curve and the characteristics of the curve of the skewed distribution is different without symmetry, this we will understand with the following example:

Example: Find the percent of score lies between 70 to 80 if the score of mathematics of university students are normally distributed with the mean 67 and standard deviation 9?

Can Normal Distribution Be Skewed
symmetry in the normal distribution or can normal distribution be skewed

Solution:

To find the percent of score we follow the probability for the normal distribution discussed earlier in normal distribution, so to do so first we will convert into normal variate and follow the table discussed in normal distribution to find the probability using the conversion

Z=(X-μ)/σ

we want to find the score percent between 70 and 80 so we use random variable values 70 and 80 with the given mean 67 and standard deviation 9 this gives

Z=70-67/9 = 0.333

and

Z=80-67/9 = 1.444

[latex]Z = \frac{70-67}{9}=0.333
\\and\\
Z = \frac{80-67}{9}=1.444[/latex]

This we can sketch as

the above shaded area shows the region between z=0.333 and z=1.444 from the table of standard normal variate the probabilities are

P(z > 0.333)=0.3707
and
P(z > 1.444)=0.0749
so
p(0.333 < z0.333)-P(z > 1.444)=0.3707-0.0749=0.2958

[latex] P(z > 0.333)=0.3707
\\and\\
P(z>1.444)=0.0749\\
so\\
p(0.333 < z0.333)-P(z> 1.444)=0.3707-0.0749=0.2958 [/latex]

so 29.58% students will score between 70 to 80 .

In the above example the skewness of the curve is zero and the curve is symmetric, to check the data is normally distributed or not we have to perform the hypothesis tests.

How do you tell if a distribution is skewed left or right?

The distribution is known to be skewed if it is right tailed or left tailed in the curve so the depending on the nature of the curve we can judge whether the distribution is positive skewed or negative skewed. The concept of skewness is discussed in detail in the articles positively and negatively skewed distribution. If the symmetry in the left side lacks the distribution is skewed left and if the symmetry lacks in the right side the distribution is skewed right. The best way to check the distribution is skewed is to check the variation in the central tendencies that is if mean<median<mode then the distribution is left skewed and if mean>median>mode then the distribution is right skewed. The geometrical representation is as follows

left skewed distribution
right skewed distribution

The measures to calculate the skewness left or right for the information given in detail in the article of skewness.

What is an acceptable skewness?

Since the skewness as earlier discussed is lack of symmetry so what range is acceptable that must be clear. The question can normal distribution is skewed arise to check whether in the normal distribution is acceptable or not and the answer of the acceptable skewness is in normal distribution because in normal distribution the skewness is zero and the distribution in which skewness is near to zero is more acceptable. So after the testing for skewness if the skewness is nearer to zero then the skewness is acceptable depending on the requirement and range for the client.

In brief the acceptable skewness is the skewness which is nearer to zero as per the requirement.

How skewed is too skewed?

The skewness is the statistical measurement to check the symmetry present in the curve of the distribution and the information and all the measures to check skewness is present or not, depending on that we can find if the distribution is far from zero then too skewed or symmetry is zero then we can say the distribution is too skewed.

How do you determine normal distribution?

To determine the distribution is normal or not we have to look the distribution have the symmetry or not if the symmetry is present and the skewness is zero then the distribution is normal distribution, the detail methods and techniques were already discussed in detail in normal distribution

Do outliers skew data?

In the distribution data if any data follow unusual way and very far or away from the usual data that is known as outlier and in most of the cases the outliers are responsible for the skewness of the distribution and because of the unusual nature of outliers the distribution have skewness, so we can say that in the distribution the outliers skew data. The outliers in all cases will not skew data they skewed data only if they also follow the systematic sequence in continuous distribution to give left or right tailed curve.

In the previous articles the detail discussion of normal distribution and skewed distribution discussed.

DR. MOHAMMED MAZHAR UL HAQUE

I am DR. Mohammed Mazhar Ul Haque , Assistant professor in Mathematics. Having 12 years of experience in teaching. Having vast knowledge in Pure Mathematics , precisely on Algebra. Having the immense ability of problem designing and solving. Capable of Motivating candidates to enhance their performance. I love to contribute to Lambdageeks to make Mathematics Simple , Interesting & Self Explanatory for beginners as well as experts. Let's connect through LinkedIn - https://www.linkedin.com/in/dr-mohammed-mazhar-ul-haque-58747899/

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