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# Skewed Data|Definition & Meaning

## Definition

Data is **skewed** when it deviates from the mean much more in one **direction** than it does in the other. **Plotting** such data results in a **non-symmetrical** graph with a long tail. For **example,** a doctor checks **thousands** of patients for cancer. Very few of these **patients** would get a positive diagnosis. In this case, the data is **heavily** skewed in favor of **negative** diagnoses.

## What Does Skewed Data Mean?

Data is **considered** skewed when it **produces** an uneven or **skewed** curve when plotted on a graph. A data set with a normal **distribution** will have a **graph** that is **symmetrical** & **shaped** like a bell when it is plotted. Skewed data, on the other hand, will **always** have a “tail” along either of the graph’s sides. The **following** are the two most **prevalent** types of skew:

### Negative Skew Data

A **data** set is said to have a **negative** skew if the graph’s tail is **located** on the **negative** side of the **graph.** This **indicates** that the **graph** is skewed to the left.

### Positive Skew Data

A **data** set is said to have a **positive** skew if the graph it **generates** has a tail just on the positive side of the **graph,** which **indicates that** the graph is skewed to the right.

A bell curve that **represents** a normal **distribution** will have a skew **value** of zero, as opposed to having either a positive or negative for **skew.** Data that is almost **symmetrical** also **contains** a skew value that is close to zero.

**Knowing** skewed data is **essential** if you are a data **scientist** or, indeed, any type of **professional** who deals with data. This is because the majority of **circumstances** that occur in the real world are not **symmetrical,** and genuine data sets are typically skewed.

**Skewed** data can, however, be **problematic** for statistical models because outliers, which are **frequently** the root cause of skew, can have a **detrimental** effect on the performance of a **statistical** model. Because of this, it is **essential** to have a good **understanding** of skewed data, **particularly** how to **compute** it.

## Examples of Data With a Skewed Distribution

The **following** are some instances from real life that should help you have a better **understanding** of both **positive** as well as **negative** skew:

### Positive Skew

A **typical** income set of data is a good **example** of data that has a positive skew. On a graph, if you construct a curve that **represents** the income of a sample group, it is likely that the curve will be **skewed** to the right, also known as being **positively** skewed.

This **will** be the case if the majority of people have **earnings** that are about **average** and a smaller percentage of people have **incomes** that are above average. The **individuals** in the data set that have high **earnings** are the ones who are considered to be outliers, which causes the curve to be **skewed** forward towards the right side of the graph.

### Negative Skew

The test **results** of a group of college students who were given a test that was not particularly difficult is an **illustration** of data that is **skewed** in an unfavorable direction. When shown on a graph, the curve that represents the **distribution** of the group of students’ test **scores** is likely to be skewed to the left.

In such a **scenario,** most students would have high test scores, while a smaller **percentage** of individuals would have low **scores,** which would cause the curve to be **skewed** toward the left **side** of the graph. The **students** who completed the test with the **lowest** scores were outliers within the **data** set, causing it to be skewed in an **unfavorable** direction.

**How To Determine the Skewness**

You can **compute** the skewness, also known as the amount of skew, in a data collection by following these four **fundamental** steps, **which** are as follows:

### Find the Average, the Median Point, and the Standard Deviation

Finding the **numbers** for three features of your data is the first step in **manually determining** skew. These are the **characteristics:**

The **average** value of a given data collection is referred to as the mean in mathematics. A **data** set’s mean can be **determined** by first **adding** all of the values in the set together & then dividing that **total** by the total number of values in the data.

The value that **corresponds** to the **point** that is **located** exactly in the **middle** of all the data points is called the **median.** You can **determine** the median of a set of values by placing all of the values in your data set in **ascending** order, from the **smallest** to the largest, and then locating the value that is exactly in the **middle** of the set.

The **standard** deviation in terms of A statistical **measurement** known as the **standard** deviation is used to **represent** the variety of **results** or the degree to which the values are **“spread** out.”

When **calculating** standard deviation for a given set of data by hand, first **determine** the mean of each of the **resulting** values, then subtract each value of the dataset from the mean (these are called deviations), squ**a**re each deviation, and sum them all. **After** that, divide by the total number of data instances.

At this **point,** you have the mean of the **square deviations,** which is called variance. Take the square root of this value, and you have the **standard deviation.**

### Plug Into the Skew Formula

After you have **determined** the mean, median, & **standard** deviation for your data, you will be able to use the skew formula to **determine** the **degree** to which your data is skewed. To get a solution for the **skew,** you can solve the equation by **entering** each of your values:

**Skewness of Data = 3 * (Mean – Median) / Standard Deviation**

### Make Sure by Using a Calculator

After **completing** the skew calculation, you can use a **graphing** calculator to verify your answer and validate that you obtained the **correct** result.

In addition, if you **would** rather not **calculate** skew by hand at all, you are free to do so and instead make use of a graphing calculator in its place. The **SKEW** function is what you want to use on a graphing calculator when **calculating** skew.

## Transform the Skewed Data You Have

You also have the option of transforming your data from a skewed distribution to a normal distribution if this becomes necessary. You have the option, dependent on the data set you’re working with, to alter skewed data using such approaches.

The process of **transforming** a data set from a skewed distribution to a normal **distribution** by employing exponents is known as the **exponential** transformation. The application of functions to data during power **transformation** might help you stabilize it, which is made **possible** thanks to power transformation.

To get a **data** set closer to having a **normal distribution,** power **transformation** is a helpful technique. Log transformation is another common method that is **utilized** in the process of transforming data sets that are favorably skewed. Log **transformation** entails applying the natural log to each value in the data set.

## A Numerical Example of Skew Data

Estimating the **Median** Skewness using Pearson’s Formula Pearson’s skewness of the annual **median** sunspot count is:

- The
**mean**is 48.6. - The median is 39.
- The
**standard**deviation is 39.5.

### Solution

**Given** that:

**Mean**is 48.6**Median**is 39- The
**standard**deviation is 39.5

We know the **formula:**

** Skewness = 3 x (Mean – Median) / Standard Deviation**

By putting values in the above **formula,** we get:

**Skewness = 3 x (48.6 – 39) / 39.5**

**= 3 x (9.6 / 39.5)**

By simplifying, we get the following:

**Skewness = 0.73**

*All mathematical drawings and images were created with GeoGebra.*