Statistics-Left Skewed And Right Skewed Distribution And Relation With Mean, Median And Mode
Summary
TLDRIn this informative video, Krishnak discusses common examples of right and left skewed distributions, such as wealth distribution and human lifespan, and explains their characteristics. He also clarifies the relationship between mean, median, and mode in these distributions, noting that in right skew, mean > median > mode, while in symmetrical distributions like normal distribution, mean ≈ median ≈ mode, and in left skew, mode > median > mean. Krishnak emphasizes the importance of practical knowledge for better understanding and explanation of these concepts.
Takeaways
- 📚 The video discusses a statistical question related to skewness in data distributions that was asked in an interview.
- 📈 The script explains the concept of right skew distribution, where the right tail of the data distribution is elongated, compared to the left.
- 💰 Wealth distribution is given as a classic example of a right skew distribution, highlighting the few extremely wealthy individuals compared to the majority with less wealth.
- ✍️ The length of comments on the speaker's YouTube channel is used as another example of a right skew distribution.
- 📊 The script contrasts right skew distribution with symmetrical (normal) distribution, which includes examples like age, weight, and height distributions.
- 🌟 Machine learning algorithms often prefer data that follows a normal distribution, as it simplifies the modeling process.
- 🔄 The left skew (or negative skew) distribution is also explained, with the lifespan of humans given as an example, where few live much longer than the average lifespan.
- 🔢 In a right skewed distribution, the mean is greater than the median, which in turn is greater than the mode.
- ⚖️ For symmetrical distributions, the mean, median, and mode are approximately equal, reflecting the balance of the data.
- 📉 In left skewed distributions, the mode is the highest, followed by the median, and then the mean, indicating the concentration of data towards the lower end.
- 🤓 The importance of understanding and being able to explain theoretical concepts with practical examples is emphasized for effective communication in interviews.
Q & A
What is the main topic discussed in the video?
-The main topic discussed in the video is the concept of right skew distribution and left skew distribution, along with examples and the relationship between mean, median, and mode in these distributions.
What is a right skew distribution?
-A right skew distribution, also known as a positively skewed distribution, is a type of distribution where the tail on the right side is longer or fatter than the left side, indicating that the data has a longer tail to the right.
Can you provide an example of a right skew distribution mentioned in the video?
-One example of a right skew distribution mentioned in the video is wealth distribution, where a few extremely wealthy individuals like Elon Musk and Jeff Bezos represent the long tail on the right side of the distribution.
What is a left skew distribution?
-A left skew distribution, also known as a negatively skewed distribution, is a type of distribution where the tail on the left side is longer or fatter than the right side, indicating that the data has a longer tail to the left.
Can you provide an example of a left skew distribution mentioned in the video?
-The lifespan of human beings is given as an example of a left skew distribution, where there are fewer people living to very old ages compared to the average lifespan, creating a longer tail on the left side.
What is the relationship between the mean, median, and mode in a right skew distribution?
-In a right skew distribution, the mean is greater than the median, and the median is greater than the mode. This is because the long tail on the right side pulls the mean to a higher value than the median.
What is the relationship between the mean, median, and mode in a left skew distribution?
-In a left skew distribution, the mode is the highest, followed by the median, and then the mean. This is because the long tail on the left side pulls the mean to a lower value than the mode.
What is a symmetrical distribution and what is an example mentioned in the video?
-A symmetrical distribution is one where the right and left sides of the distribution are mirror images of each other. An example mentioned in the video is the normal distribution, which is often seen in features like age, weight, and height in datasets.
What is the relationship between the mean, median, and mode in a symmetrical distribution?
-In a symmetrical distribution, the mean, median, and mode are approximately equal, as the distribution is balanced with no skew to either side.
Why is it important to understand the relationship between mean, median, and mode in different types of distributions?
-Understanding the relationship between mean, median, and mode in different distributions is important because it helps in interpreting the data correctly. It can indicate the presence of outliers, the central tendency, and the skewness of the data, which are crucial for data analysis and decision-making.
How can one remember the relationship between mean, median, and mode in different distributions?
-One can remember the relationship by visualizing the distribution diagrams and associating the positions of mean, median, and mode with the direction of the skew. For right skew, mean > median > mode; for symmetrical, mean ≈ median ≈ mode; for left skew, mode > median > mean.
Outlines
📊 Introduction to Skewness in Data Distribution
Krishnak introduces a statistical question from a recent interview, focusing on right and left skew distributions. He explains the concept of skewness by describing the shape of a histogram or kernel density estimator and provides examples of right-skewed data, such as wealth distribution featuring billionaires like Elon Musk and Bill Gates. He also mentions the length of comments on his YouTube channel as another example. The explanation is aimed at helping viewers understand the basic concept of skewness and its practical applications.
📚 Understanding Mean, Median, and Mode in Skewed Distributions
The second paragraph delves into the relationship between mean, median, and mode in different types of distributions. Krishnak clarifies that in a right-skewed distribution, the mean is greater than the median, which in turn is greater than the mode. For a symmetrical distribution, like the normal distribution, the mean, median, and mode are approximately equal. In contrast, for a left-skewed or negative skew distribution, the mode is the highest, followed by the median and then the mean. Krishnak emphasizes the importance of knowing examples to explain these concepts effectively and encourages viewers to apply theoretical knowledge to practical scenarios.
Mindmap
Keywords
💡Right Skew Distribution
💡Left Skew Distribution
💡Symmetric Distribution
💡Mean
💡Median
💡Mode
💡Histogram
💡Kernel Density Estimator
💡Interview Question
💡Comment Length
💡Iris Dataset
Highlights
Introduction to the YouTube channel and the purpose of sharing interview questions.
The importance of uploading interview questions to an interview playlist for future reference.
A recent interview question about classical examples of right and left skew distributions.
Explanation of what constitutes a right skew distribution in data.
Wealth distribution as a classical example of a right skew distribution.
Length of comments on videos as an example of right skew distribution.
Introduction to symmetrical distribution, also known as normal distribution.
Examples of normal distribution in features of machine learning algorithms.
Iris dataset features following a normal distribution.
Definition and explanation of left skew or negative skew distribution.
Lifespan of humans as an example of a left skew distribution.
The relationship between mean, median, and mode in right skew distribution.
Mean being greater than median, which in turn is greater than mode in right skew distribution.
Mean, median, and mode being approximately equal in symmetrical distribution.
In left skew distribution, mode is the highest, followed by median and then mean.
The significance of understanding and remembering examples for explaining theoretical concepts.
Encouragement for viewers to subscribe to the channel for more interview question insights.
Transcripts
hello all my name is krishnak and
welcome to my youtube channel so guys
morning ad actually asked you a
statistical question which was recently
asked
in an interview to one of my subscriber
as you all know guys
most of the interview questions
whichever i get to know i am definitely
uploading that in my interview playlist
and whenever i find out any new
questions i'll probably make a video
with respect to that
so let me just tell you what was the
question basically asked and for that
in the morning also i had actually
created a video many of you
actually gave the right answer and yes
many of you were also actually confused
okay with respect to the question that i
had asked so the question was that
just tell us some of the classical
examples of
the right skew distribution and the left
skid distribution
and the second question was that what is
the relationship between the mean
median mode of right skill distribution
and the left skill distribution now
first of all we'll try to understand
what exactly is right skew distribution
and left skill distribution
now guys whatever data you take and
probably if you're trying to
plot it in the form of histogram in the
form of
kernel density estimator and whenever
you see
this kind of right hand side elongated
line right like this like this kind of
distribution this is basically called as
right skewed data okay
that basically means your right side
right hand side of this particular curve
is little bit elongated when compared to
the left hand side right
now some of the classical examples over
here so i'm just going to take some of
the example
the first example that i would like to
take is wealth
distribution this is a very classical
example
which recruiters also like to hear just
imagine some of the top most richest
people like elon musk
jeff from amazon mark zuckerberg bill
gates they usually fall in this
particular region
even ambani and they are very less
number of people
you know who follows in this specific
reason whereas
in this particular region you will be
finding people with the same amount of
wealth
right this is one classical example the
second classical example that i would
like to take
is probably you can you know that like
you have seen my channel you have seen
most of my videos guys you'll be seeing
that some of the people like to
write a longer comments right probably
after seeing a video
so length of the comments
length of comments probably in my video
this is also a classical example
right so here you'll be seeing that some
of the people will be writing
longer comments they are also some of
the people who will be writing smaller
comments and some of the people
will most of the people will be writing
medium size comment probably one liner
right so this is two classical examples
that i want to give
yes in the morning video many people
gave some amazing examples itself
right and you should also check out that
again the link will be given in
description
now coming to the second uh distribution
second distribution which is called a
symmetrical distribution this is nothing
but our
normal distribution this is the example
normal distribution i think we have
worked out normal distribution with
respect to our machine learning problem
statement
i'll get some of the algorithms once all
of the features falling in this kind of
most of the features falling in this
kind of distribution itself
some of the classical example is that
age distribution
probably weight distribution uh
probably height distribution they all
follow this kind of normal distribution
and even if you have worked with iris
data set you saw that in the iris data
set you had features like petal length
petalwidth sepal length and
weight right that was also following
this kind of normal distribution
and remember guys most of the machine
learning algorithm likes the data
to have this kind of normal distribution
property or
and why it is called a symmetrical
distribution because the right hand
curve
will almost be equal to the left hand
curve okay
so these are like mirror phase fine
coming to the third kind of distribution
which is also called as
left cube distribution it is also called
as negative skew distribution
here the left hand side will be little
bit elongated
and then the right hand side right so
here the perfect example i'll say
lifespan of human being
lifespan of human being
because there are many people if i talk
about the average lifespan
it is somewhere around 50 to 70 so 50 to
70 will basically be falling in this
particular region
there will be people who will be dying
quite early in the age
but they will be also very less number
of people who will be living more than
70 years probably near 100 and all
again a perfect example to make you
understand yes
if you have some more examples
definitely many people had also written
in the morning
and i i like most of the examples itself
right
now coming to the second question what
is the exact relationship with respect
to mean median and mode
it is very very much simple just by
seeing this particular diagram i think
you will be able to know it guys
mean in the right skewed distribution
over here will be greater than median
and median will be greater than mode
right so mean will be greater than
median and median will be greater than
mode so this is the exact relationship
that you will be able to find
just by seeing this particular diagram
will be able to understand in the case
of symmetrical distribution
mean will be approximately equal to
median it will be approximately equal to
mode so this is the second relationship
that you find out with respect to normal
distribution
the third one basically what you see
over here if i take this particular
example over here your mode is highest
then your median then your
mean right so this is the exact
relationship let me just write it down
if you are getting confused
first the highest will be mode
then your median you have because median
will be obviously smaller than mode
then you have mean so this is the
relationship that you find out with
respect to the
negative skewed data so this
is what the interviewer may be expecting
probably remember whenever this kind of
questions are asked always make sure
that you know some of the examples
because if you tend to forget this
particular topics also
just with the help of those examples
will be able to explain it in a proper
way
trust me guys practical knowledge
definitely understanding of that
theoretical is very very much important
if you are able to relate this
theoretical thing with some practical
stuff
you will be able to understand you will
be able to relate once you able to
relate it
you will be able to understand you will
be able to explain it okay
so this is what i really wanted to cover
just let me know whether
you like this kind of thing or not
because every day i'll at least come up
with one interview questions probably
and then i'll try to explain you
completely from end to end so i hope you
like this particular video please do
subscribe the channel if you're not
already subscribed i'll see you in the
next video have a great day ahead
thank you and all bye
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