This article shows you how to calculate the standard deviation of a given list of numerical values in Python.

Table of Contents

## Definition and Problem Formulation

The standard deviation is defined as the *square root of the variance*.

In case you’ve attended your last statistics course a few years ago, let’s quickly recap the **definition of variance**: variance is the *average squared deviation of the list elements from the average value.*

Standard deviation is simply the square root of the variance.

**So, how to calculate the standard deviation of a given list in Python?**

## Solution Overview

Here are three methods to accomplish this:

**Method 1**: Import the NumPy library with`import numpy as np`

and call`np.std(list)`

.**Method 2**: Import the`statistics`

library with`import statistics`

and call`statistics.stdev(list)`

to obtain a slightly different result because it’s normalized with*(n-1)*rather than*n*for*n*list elements — this is called Bessel’s correction.**Method 3**: In vanilla Python without external dependency, calculate the average as`avg = sum(list)/len(list)`

and then calculate the variance using the one-liner`(sum((x-avg)**2 for x in lst) / len(lst))**0.5`

.

In addition to these three methods, we’ll also show you how to compute the standard deviation in a Pandas DataFrame in **Method 4**.

But before we do this, let’s examine the first three methods in one Python code snippet:

lst = [1, 0, 1, 2] # 1. NumPy Standard Deviation import numpy as np std = np.std(lst) print(std) # 0.7071067811865476 # 2. Statistics Standard Deviation import statistics std = statistics.stdev(lst) print(std) # 0.816496580927726 # 3. W/O External Dependency avg = sum(lst) / len(lst) var = sum((x-avg)**2 for x in lst) / len(lst) std = var**0.5 print(std) # 0.7071067811865476

Let’s dive into each of those methods next.

## Method 1: Standard Deviation in NumPy Library

import numpy as np lst = [1, 0, 1, 2] std = np.std(lst) print(std) # 0.7071067811865476

In the first example, you create the list and pass it as an argument to the `np.std(lst)`

function of the NumPy library.

π‘ **Note**: Python’s package for data science computation NumPy also has great statistics functionality. Specifically, the NumPy library also supports computations on basic collection types, not only on NumPy arrays. You can calculate all basic statistics functions such as average, median, variance, and standard deviation on NumPy arrays.

If you need to improve your NumPy skills, check out our in-depth blog tutorial.

You can also calculate the standard deviation of a NumPy array instead of a list by using the same method:

Simply import the NumPy library and use the `np.std(a)`

method to calculate the average value of NumPy array `a`

.

Here’s the code:

import numpy as np a = np.array([1, 2, 3]) print(np.std(a)) # 0.816496580927726

## Method 2: Standard Deviation in Statistics Library

import statistics lst = [1, 0, 1, 2] std = statistics.stdev(lst) print(std) # 0.816496580927726

In the second example, you calculate the standard devaition as follows.

Import the `statistics`

library and call the function `statistics.stdev(lst)`

to calculate the standard deviation of a given list `lst`

. The only difference to the NumPy standard deviation is that the Bessel’s correction is applied: the result is divided by *(n-1)* rather than *n*.

If you need more background on this, click this wiki link.

Standard deviation is defined as the deviation of the data values from the average (wiki). It’s used to measure the dispersion of a data set.

## Method 3: Vanilla Python Standard Deviation

lst = [1, 0, 1, 2] avg = sum(lst) / len(lst) var = sum((x-avg)**2 for x in lst) / len(lst) std = var**0.5 print(std) # 0.7071067811865476

In the third example, you first calculate the average as ** sum(list)/len(list)**.

Then, you use a generator expression (see list comprehension) to dynamically generate a collection of individual squared differences, one per list element, by using the expression `(x-avg)**2`

.

You sum them up and normalize the result by dividing through the number of list elements to obtain the variance.

## Method 4: Standard Deviation in Python Pandas

Want to calculate the standard deviation of a column in your Pandas DataFrame?

You can do this by using the `pd.std()`

function that calculates the standard deviation along all columns. You can then get the column you’re interested in after the computation.

import pandas as pd # Create your Pandas DataFrame d = {'username': ['Alice', 'Bob', 'Carl'], 'age': [18, 22, 43], 'income': [100000, 98000, 111000]} df = pd.DataFrame(d) print(df)

Your DataFrame looks like this:

username | age | income | |

0 | Alice | 18 | 100000 |

1 | Bob | 22 | 98000 |

2 | Carl | 43 | 111000 |

Here’s how you can calculate the standard deviation of all columns:

print(df.std())

The output is the standard deviation of all columns:

age 13.428825 income 7000.000000 dtype: float64

To get the variance of an individual column, access it using simple indexing:

print(df.std()['age']) # 180.33333333333334

## Related Questions

This is the absolute minimum you need to know about calculating basic statistics such as the standard deviation (and variance) in Python.

But there’s far more to it and studying the other ways and alternatives will actually make you a better coder.

So, let’s dive into some related questions and topics you may want to learn!

### Python List Median

What’s the median of a Python list? Formally, the median is “the value separating the higher half from the lower half of a data sample” (wiki).

#### How to calculate the median of a Python list?

- Sort the list of elements using the
`sorted()`

built-in function in Python. - Calculate the index of the middle element (see graphic) by dividing the length of the list by 2 using integer division.
- Return the middle element.

Together, you can simply get the median by executing the expression `median = sorted(income)[len(income)//2]`

.

Here’s the concrete code example:

income = [80000, 90000, 100000, 88000] average = sum(income) / len(income) median = sorted(income)[len(income)//2] print(average) # 89500.0 print(median) # 90000.0

**Related tutorials:**

### Python List Mean

The mean value is exactly the same as the average value: sum up all values in your sequence and divide by the length of the sequence.

You can use either the calculation `sum(list) / len(list)`

or you can import the `statistics`

module and call `mean(list)`

.

Here are both examples:

lst = [1, 4, 2, 3] # method 1 average = sum(lst) / len(lst) print(average) # 2.5 # method 2 import statistics print(statistics.mean(lst)) # 2.5

Both methods are equivalent. The `statistics`

module has some more interesting variations of the `mean()`

method (source):

`mean()` | Arithmetic mean (βaverageβ) of data. |

`median()` | Median (middle value) of data. |

`median_low()` | Low median of data. |

`median_high()` | High median of data. |

`median_grouped()` | Median, or 50th percentile, of grouped data. |

`mode()` | Mode (most common value) of discrete data. |

These are especially interesting if you have two median values and you want to decide which one to take.

### Python List Min Max

There are Python built-in functions that calculate the minimum and maximum of a given list. The `min(list)`

method calculates the minimum value and the `max(list)`

method calculates the maximum value in a list.

Here’s an example of the minimum, maximum, and average computations on a Python list:

import statistics as s lst = [1, 1, 2, 0] average = sum(lst) / len(lst) minimum = min(lst) maximum = max(lst) print(average) # 1.0 print(minimum) # 0 print(maximum) # 2

## Where to Go From Here

**Summary**: how to calculate the standard deviation of a given list in Python?

- Import the NumPy library with
`import numpy as np`

and use the`np.std(list)`

function. - Import the
`statistics`

library with`import statistics`

and call`statistics.stdev(list)`

to obtain a slightly different result because it’s normalized with (n-1) rather than n for n list elements – this is called Bessel’s correction. - Without External Dependency: Calculate the average as
`sum(list)/len(list)`

and then calculate the variance in a list comprehension statement.

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