Skewness and kurtosis are two important measure in statistics. Skewness refers the lack of symetry and kurtosis refers the peakedness of a distribution.

## Skewness

- Mean, median, mode fall at different points, i.e, Mean ≠ Median ≠ Mode.
- Quartiles are not equidistant from median.
- The curve drawn with the help of the given data is not symmetrical but stretched more to one side than the other.

The lack of symmetry in a distribution is always determined with reference to a normal distribution, which is always symmetrical. Any departure of a distribution from symmetry leads to an asymmetric distribution and in such cases, we call this distribution as skewed. The skewness may be either positive or negative. Absence of skewness makes the distribution symmetrical.

It is important to emphasize that skewness of a distribution cannot be determined simply by inspection. If we understand the differences between the mean, median and the mode, we should be able to suggest a direction of skew.We can define the skewness of a frequency distribution in three different shapes as following-

**(1). Symmetrical distributions**

**(2). Positively skewed distributions**

**(3). Negatively skewed distributions**

### Measures of skewness

**Skewness(p)= (Mean-Mode) / Standard Deviation**

- If mean > mode, the distribution is positively skewed.
- If mean < mode, the distribution is negatively skewed.
- If mean = mode, the distribution is not skewed or symmetrical.

**Skewness(p)= 3(Mean-Mode) / Standard Deviation**

### Kurtosis

### Measures of kurtosis

- If kurtosis>3, the distribution is leptokurtic.
- If kurtosis<3, the distribution is platykurtic.
- If kurtosis=3, the distribution is mesokurtic.

#### 1. Mesokurtic

Data that follows a mesokurtic distribution shows an excess kurtosis of zero or close to zero. This means that if the data follows a normal distribution, it follows a mesokurtic distribution.

#### 2. Leptokurtic

Leptokurtic indicates a positive excess kurtosis. The leptokurtic distribution shows heavy tails on either side, indicating large outliers. In finance, a leptokurtic distribution shows that the investment returns may be prone to extreme values on either side. Therefore, an investment whose returns follow a leptokurtic distribution is considered to be risky.

#### 3. Platykurtic

A platykurtic distribution shows a negative excess kurtosis. The kurtosis reveals a distribution with flat tails. The flat tails indicate the small outliers in a distribution. In the finance context, the platykurtic distribution of the investment returns is desirable for investors because there is a small probability that the investment would experience extreme returns.

**Try some fresh content:**

Thank you a lot for sharing this with all of us you actually recognize what you’re speaking about! Bookmarked. Kindly additionally consult with my web site =). We could have a link change agreement between us!

Nice read, I just passed this onto a friend who was doing a little research on that. And he just bought me lunch because I found it for him smile Therefore let me rephrase that: Thank you for lunch!

I’m really impressed along with your writing skills as well as with the format in your weblog. Is that this a paid theme or did you customize it your self? Either way stay up the excellent quality writing, it抯 rare to see a nice weblog like this one nowadays..

Thanks for your handy post. Through the years, I have been able to understand that the particular symptoms of mesothelioma are caused by a build up connected fluid between your lining in the lung and the torso cavity. The sickness may start inside the chest vicinity and pass on to other limbs. Other symptoms of pleural mesothelioma cancer include weight reduction, severe breathing trouble, nausea, difficulty taking in food, and infection of the neck and face areas. It must be noted that some people with the disease do not experience any serious signs or symptoms at all.

Best view i have ever seen !

What i don’t realize is actually how you’re

now not actually much more neatly-favored than you might be right now.

You’re so intelligent. You understand therefore significantly when it comes to this subject, produced me personally imagine it from numerous various

angles. Its like men and women are not fascinated until it’s

something to do with Lady gaga! Your personal stuffs outstanding.

At all times handle it up!

It’s a pity you don’t have a donate button! I’d most certainly

donate to this excellent blog! I suppose for now i’ll settle for

book-marking and adding your RSS feed to my Google

account. I look forward to fresh updates and will share this site with

my Facebook group. Talk soon!

My partner and I absolutely love yor blog and

find the majority of your post’s tto be precisely what I’m looking for.

Would you offer guest writers to write content tto suit your needs?

I wouldn’t mind creating a post orr elaborating on some of the subjects you write about here.

Again, awesome weblog!

My spouse and I stumbled over here from a different website and thought I might check things

out. I like what I see so now i’m following you. Look forward to exploring your

web page again.

bookmarked!!, I like your site!

Hey would you mind letting me know which webhost you’re using? I’ve loaded your blog in 3 completely different browsers and I must say this blog loads a lot quicker then most. Can you suggest a good hosting provider at a reasonable price? Thank you, I appreciate it!

I am very happy to read this. This is the kind of manual that needs to be given and not the accidental misinformation that is at the other blogs. Appreciate your sharing this best doc.

I am truly happy to glance at this weblog posts which consists

of lots of valuable data, thanks for providing these

kinds of information.

Spot on with this write-up, I truly think this website wants way more consideration. I抣l most likely be again to learn much more, thanks for that info.

Hi colleagues, its enormous piece of writing about educationand

completely explained, keep it up all the time.