To calculate the standard deviation of a row, we need to set the axis parameter to axis=1 or columns. Syntax: DataFrame/Series.std (self, axis=None, skipna=None, level=None, ddof=1, numeric_only=None, **kwargs) Parameters: axis: {index (0), columns (1)} skipna: This parameters takes bool value, default value is True. At first, import the required Pandas library , Now, create a DataFrame with two columns , Finding the standard deviation of Units column value using std() . Exclude NA/null values. Let's write the code to calculate the mean and standard deviation in Python. By default, it uses the EMA. Installation: pip install scipy. You can use .std(axis=1) [pandas-doc] instead, this will result in a Series with as indices the indices of your dataframe, and as values, the standard deviation of the two values in the corresponding columns: Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. How to Calculate Standard Deviation in Pandas (With Examples) You can use the DataFrame.std () function to calculate the standard deviation of values in a pandas DataFrame. In Python, we can declare a data set with the help of the list. pandas.DataFrame.std# DataFrame. Without a subpoena, voluntary compliance on the part of your Internet Service Provider, or additional records from a third party, information stored or retrieved for this purpose alone cannot usually be used to identify you. How to Calculate the Coefficient of Variation in Python. The volatility is defined as the annualized standard deviation. In respect to calculate the standard deviation, we need to import the package named " statistics " for the calculation of median. We will use the statistics module and later on try to write our own . Help us identify new roles for community members, Proposing a Community-Specific Closure Reason for non-English content, Create a Pandas Dataframe by appending one row at a time. will calculate the standard deviation of the dataframe across columns so the output will, Score1 17.446021 we can calculate standard deviation by sqrt of variance it will give some measure about, how far elements from the mean. [duplicate]. Below is the implementation: # importing pandas import pandas as pd # given list given_list = [34, 14, 7, 13, 26, 22, 12, 19, 29, 33, 31, 30, 20, 10, 9 . Syntax of standard deviation Function in python DataFrame.std(axis=None, skipna=None, level=None, ddof=1, numeric_only=None) Parameters : axis :{rows (0), columns (1)} skipna :Exclude NA/null values when computing the result level :If the axis is a MultiIndex (hierarchical), count along a particular level, collapsing into a Series ; scale: optional (default=1), represents standard . Upon calculating the coefficient of variation for each fund, the investor finds: . The technical storage or access that is used exclusively for statistical purposes. Examples - Let's create a dataset to work with. This can be changed using the ddof argument. The Python Pandas library provides a function to calculate the standard deviation of a data set. Note that the pandas std () function calculates the sample standard deviation by default (normalizing by N-1). A list is nothing but a special variable that can store multiple data. Remove Outliers from Dataframe using pandas in Python. You can do this by using the pd.std () function that calculates the standard deviation along all columns. Then, you can use the numpy is std () function. import pandas as pd # Create your Pandas DataFrame d = {'username': ['Alice', 'Bob', 'Carl'], The divisor used in calculations is N ddof, where N represents the number of elements. From here, calculating the standard deviation is as simple as applying .std () to our DataFrame, as seen in Finding Descriptive Statistics for Columns in a DataFrame: std_pandas = df.std() std_pandas 0 8.379397 dtype: float64 Calculating std of numbers with Pandas But wait this isn't the same as our hand-calculated standard deviation! The standard deviation is usually calculated for a given column and it's normalised by N-1 by default. import pandas as pd import numpy as np import matplotlib.pyplot as plt import pandas_datareader as web Individual Stock Downloading the stock price for Netflix Netflix has seen phenomenal growth since 2009. How can I use a VPN to access a Russian website that is banned in the EU? Find centralized, trusted content and collaborate around the technologies you use most. Delta Degrees of Freedom. We do not currently allow content pasted from ChatGPT on Stack Overflow; read our policy here. Here we discuss how we plot errorbar with mean and standard deviation after grouping up the data frame with certain applied conditions such that errors become more truthful to make necessary for obtaining the best results and visualizations. In this tutorial we will learn, skipna : Exclude NA/null values when computing the result, level : If the axis is a MultiIndex (hierarchical), count along a particular level, collapsing into a Series. How I can calculate standard deviation for rows of a dataframe? numeric_only : Include only float, int, boolean columns. I have used this : But this gives me the standard deviation for the whole dataframe i am afraid. Manage SettingsContinue with Recommended Cookies. GradientBoostingRegressor Text Classifier. If None, will attempt to use everything, then use only numeric data. First, we generate the random data with mean of 5 and standard deviation (SD) of 1. I have a datset with Scores and Categories and I would like to calculate the Standard Deviation of these scores, per category. In statistics standard deviation is the average amount of variability in your data set. We make use of First and third party cookies to improve our user experience. Not consenting or withdrawing consent, may adversely affect certain features and functions. Using the Statistics Module The statistics module has a built-in function called stdev, which follows the syntax below: standard_deviation = stdev ( [data], xbar) [data] is a set of data points Modules Needed: pip install numpy pip install pandas pip install matplotlib. Calculate mean and standard deviation of returns Lets load the modules first. The first function takes the data of an entire population and returns its standard deviation. Variance and Standard Deviation in SAS Row wise and column, Row wise Standard deviation row Standard deviation in R, Mean, Variance and standard deviation of column in Pyspark, STDEVP Function in Excel - Calculate the Population Standard, Tutorial on Excel Trigonometric Functions, How to find the standard deviation of a given set of numbers, How to find standard deviation of a dataframe in pandas, How to find the standard deviation of a column in pandas dataframe, How to find row wise standard deviation of a pandas dataframe. Standard deviation tells about how the values in the dataset are spread. The page is structured as follows: 1) Example 1: Standard Deviation of List Object 2) Example 2: Standard Deviation of One Particular Column in pandas DataFrame 3) Example 3: Standard Deviation of All Columns in pandas DataFrame ax1 = plt.subplot(2, 1, 1) df['Close'].plot() This is new! Another interesting visualization would be to compare the Texas HPI to the overall HPI. You can use the DataFrame.std() function to calculate the standard deviation of values in a pandas DataFrame. Calculates the standard deviation of values by using DataFrame/Series.std () method. Standard deviation is calculated using the function .std(). Agree Pandas DataFrame sum() method with examples. To calculate the standard deviation we need to provide a data set. Notes. Step 3: Visualize the Volatility of Historic Stock Prices This can be visualized with Matplotlib. We need to use the package name statistics in calculation of median. 4 You can use .std (axis=1) [pandas-doc] instead, this will result in a Series with as indices the indices of your dataframe, and as values, the standard deviation of the two values in the corresponding columns: >>> df.std (axis=1) 0 1.414214 1 2.687006 2 1.626346 3 1.223295 4 1.025305 5 1.732412 6 1.965757 dtype: float64 Share Improve this answer How to Calculate Variance in Python Pandas ? We will compare mean, standard deviation and coefficient of. In this post, I'll illustrate how to calculate the standard deviation in Python. Not the answer you're looking for? using the statistics module the statistics module has a built in function called stdev, which follows the syntax below: standard deviation = stdev ( [data], xbar) [data] is a set of data points. Mathematica cannot find square roots of some matrices? Next we will calculate the portfolio mean and standard deviation, this is simple with the pandas module. Python and Pandas allow us to quickly use functions to obtain important statistical values from mean to standard deviation. You can change the degrees of freedom using the ddof parameter. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. ddof :Delta Degrees of Freedom. In the following examples, we are going to work with Pandas groupby to calculate the mean, median, and standard deviation by one group. I just want to get the error for each data point and plot the error bars, so i am looking to calculate the standard deviation for each row. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page. Score2 17.653225 Sometimes, it may be required to get the standard deviation of a specific column that is numeric in nature. import numpy as np import pandas as pd #define . Example 1 : Finding the mean and Standard Deviation of a Pandas Series. A Computer Science portal for geeks. You can calculate the standard deviation of a single column like this, or you can calculate the standard deviation for all the columns like this. It tells you on average how far each score lies from the mean. By default it is normalized by N-1. groupby ( ['a'], as_index=False).agg . Also, here's a link to the official documentation. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. It's not too hard though. If you want to calculate the sample standard deviation, you would have to specify the ddof argument within the std function to be equal to 1. Want to calculate the standard deviation of a column in your Pandas DataFrame? Use the rolling () Function to Calculate the Rolling Standard Deviation Statistics is a big part of data analysis, and using different statistical tools reveals useful information. Is energy "equal" to the curvature of spacetime? How does the Chameleon's Arcane/Divine focus interact with magic item crafting? The following examples shows how to use each method with the following pandas DataFrame: The following code shows how to calculate the standard deviation of one column in the DataFrame: The standard deviation turns out to be 6.1586. The following code shows how to calculate the standard deviation of multiple columns in the DataFrame: The standard deviation of the points column is 6.1586and the standard deviation of the rebounds column is 2.5599. assists 2.549510 using the statistics module the statistics module has a built in function called stdev, which follows the syntax below: standard deviation = stdev ( [data], xbar) [data] is a set of data points. volatility = data ['Log returns'].std ()*252**.5 Notice that square root is the same as **.5, which is the power of 1/2. Consenting to these technologies will allow us to process data such as browsing behavior or unique IDs on this site. The statistics module of Python also provides functions to calculate the standard deviation in two different variations. You can then get the column you're interested in after the computation. Japanese girlfriend visiting me in Canada - questions at border control? In the same way, we have calculated the standard deviation from the 2nd DataFrame. Pandas Groupby Mean If we want to calculate the mean salary grouped by one column (rank, in this case) it's simple. To calculate the standard deviation, use the std() method of the Pandas. At first, import the required Pandas library import pandas as pd Now, create a DataFrame with two columns dataFrame1 = pd. Why is this usage of "I've to work" so awkward? Learn more about us. Python Text Classification - Data that does not fit into any category. Follow the below code example to perform the action: Here, you can see that we have calculated the standard deviation of a data set from 1 to 5. Why is the federal judiciary of the United States divided into circuits? Pandas is a library in Python that is used to calculate the standard deviation. To see an example, check out our tutorial on calculating standard deviation in Python. The data look something like this: . Program: pandas.core.window.rolling.Rolling.std # Rolling.std(ddof=1, numeric_only=False, *args, engine=None, engine_kwargs=None, **kwargs) [source] # Calculate the rolling standard deviation . This is because pandas calculates the sample standard deviation by default (normalizing by N - 1). Is there any reason on passenger airliners not to have a physical lock between throttles. You can use the following methods to calculate the standard deviation in practice: Method 1: Calculate Standard Deviation of One Column, Method 2: Calculate Standard Deviation of Multiple Columns, Method 3: Calculate Standard Deviation of All Numeric Columns. The Pandas std () is defined as a function for calculating the standard deviation of the given set of numbers, DataFrame, column, and rows. We can find pstdev () and stdev (). Not implemented for Series. To get the population standard deviation, pass ddof = 0 to the std () function. What's the \synctex primitive? The divisor used in calculations is N-ddof, where N represents the number of elements. The pstdev () and stdev () return the standard deviation by taking the data of an entire population and from any sample respectively. rebounds 2.559994 In the following code chunk, there is a function that you can use to calculate RSI, using nothing but plain Python and pandas. The technical storage or access is strictly necessary for the legitimate purpose of enabling the use of a specific service explicitly requested by the subscriber or user, or for the sole purpose of carrying out the transmission of a communication over an electronic communications network. To provide the best experiences, we use technologies like cookies to store and/or access device information. Get list from pandas dataframe column or row? You pass the function a DataFrame, the number of periods you want the RSI to be based on and if you'd like to use the simple moving average (SMA) or the exponential moving average (EMA). 683 subscribers This tutorial explains how to use the Python Pandas library to calculate the Standard Deviation of a dataset. The technical storage or access is necessary for the legitimate purpose of storing preferences that are not requested by the subscriber or user. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. pandas.DataFrame.std. Python We may conduct different statistics operations on the data values using the Pandas module, one of which is standard deviation, as shown below. The std () function of the NumPy library is used to calculate the standard deviation of the elements in a given array (list). Standard deviation (): The standard deviation measures the spread of the data about the mean value. We just use Pandas mean method on the grouped dataframe: df_rank['salary'].mean().reset_index(). Statology Study is the ultimate online statistics study guide that helps you study and practice all of the core concepts taught in any elementary statistics course and makes your life so much easier as a student. import pandas s = pandas.Series ( [12, 43, 12, 53]) s.std () If you need to calculate the population standard deviation, just pass in an additional ddof argument like below. We can calculate standard devaition in pandas by using pandas.DataFrame.std () function. Code. How to Calculate the Max Value of Columns in Pandas, Your email address will not be published. How does legislative oversight work in Switzerland when there is technically no "opposition" in parliament? Standard Deviation Function In Python Pandas Dataframe Row And Column. DataFrame ( { "Car": ['BMW', 'Lexus', 'Audi', 'Tesla', 'Bentley', 'Jaguar'], "Units": [100, 150, 110, 80, 110, 90] } ) Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. How to calculate standard deviation in python: . #calculate standard deviation of 'points' column, #calculate standard deviation of 'points' and 'rebounds' columns, The standard deviation of the points column is, #calculate standard deviation of all numeric columns, points 6.158618 To calculate the coefficient of variation for a dataset in Python, you can use the following syntax: . The Pandas DataFrame std () function allows to calculate the standard deviation of a data set. dtype: float64, axis=0 argument calculates the column wise standard deviation of the dataframe so the result will be, axis=1 argument calculates the row wise standard deviation of the dataframe so the result will be, The above code calculates the standard deviation of the Score1 column so the result will be. rev2022.12.9.43105. dtype: float64, How to Find Quartiles Using Mean & Standard Deviation. Where is it documented? # finding the mean How to iterate over rows in a DataFrame in Pandas, Deleting DataFrame row in Pandas based on column value, How to deal with SettingWithCopyWarning in Pandas. Let's find out how. How to do this? How to calculate standard deviation with pandas for each row? How it works. Standard deviation Function in python pandas is used to calculate standard deviation of a given set of numbers, Standard deviation of a data frame, Standard deviation of column or column wise standard deviation in pandas and Standard deviation of rows, lets see an example of each. Required fields are marked *. How to connect 2 VMware instance running on same Linux host machine via emulated ethernet cable (accessible via mac address)? To compute the population std: def pop_std (x): return x.std (ddof=0) result = df. Next, we make our standard deviation column: df['STD'] = pd.rolling_std(df['Close'], 25, min_periods=1) Hey, that was easy! . ; loc : optional (default=0), represents mean of the distribution. Example 2: Standard Deviation by Group & Subgroup in pandas DataFrame. # calculating the median abolute deviation using pandas import pandas as pd from scipy.stats import median_abs_deviation numbers = [ 86, 60, 95, 39, 49, 12, 56, 82, 92, 24, 33, 28, 46, 34, 100, 39, 100, 38, 50, 61, 39, 88, 5, 13, 64 ] df = pd.dataframe (numbers, columns= [ 'numbers' ]) print (df [ [ 'numbers' ]].apply (median_abs_deviation)) # The divisor used in calculations is N - ddof, where N represents the number of elements. The following tutorials explain how to perform other common operations in pandas: How to Calculate the Mean of Columns in Pandas import pandas s = pandas.Series ( [12, 43, 12, 53]) s.std (ddof=0) Calculate for Pandas DataFrame This is where the std () function can be used. The second function takes data from a sample and returns an estimation of the population standard deviation. The following code shows how to calculate the standard deviation of every numeric column in the DataFrame: Notice that pandas did not calculate the standard deviation of the team column since it was not a numeric column. How to find the standard deviation of specific columns in a dataframe in Pandas Python? I want to calculate the standard deviation for each row (as in between 2 data points). Pandas : compute mean or std (standard deviation) over entire dataframe, pandas create new column based on values from other columns / apply a function of multiple columns, row-wise. The easiest way to calculate standard deviation in python is to use either the statistics module or the numpy library. DataScience Made Simple 2022. Mutual Fund B: mean = 5%, standard deviation = 8.2%. # get the standard deviation print(col.std(ddof=0)) Output: 3.8078865529319543 Now we get the same standard deviation as the above two examples. Your email address will not be published. The std () method in pandas calculates the sample standard deviation over requested axis. numpy standard deviation; pandan jaya lrt; pandas cumulative mean; pandas find median of non zero values in a column; pandas interpolate string; percentage true in pandas series; python - caculate the average based on the level of a second column in a df; python standard deviation; rolling std dev of a pandas series; standard deviation in . To normalize by N, we need to set the ddof=0. std (axis = None, skipna = True, level = None, ddof = 1, numeric_only = None, ** kwargs) [source] # Return sample standard deviation over requested axis. The square root of the variance (calculated above) is the standard deviation. The consent submitted will only be used for data processing originating from this website. Python - Calculate the variance of a column in a Pandas DataFrame, Python - Calculate the maximum of column values of a Pandas DataFrame, Python - Calculate the minimum of column values of a Pandas DataFrame, Python - Calculate the mean of column values of a Pandas DataFrame, Python - Calculate the median of column values of a Pandas DataFrame, Python - Calculate the count of column values of a Pandas DataFrame, Python Program to Calculate Standard Deviation, Python Group and calculate the sum of column values of a Pandas DataFrame, Print the standard deviation of Pandas series, C program to calculate the standard deviation, C++ Program to Calculate Standard Deviation, Java Program to Calculate Standard Deviation, Python Create a new column in a Pandas dataframe, Python Pandas - Draw a bar plot and show standard deviation of observations with Seaborn. How did muzzle-loaded rifled artillery solve the problems of the hand-held rifle? However, the Pandas library creates the Dataframe object and then the function .std() is applied on that Dataframe. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. The easiest way to calculate standard deviation in Python is to use either the statistics module or the Numpy library. The technical storage or access that is used exclusively for anonymous statistical purposes. Received a 'behavior reminder' from manager. How to Calculate the Mean of Columns in Pandas, How to Calculate the Median of Columns in Pandas, How to Calculate the Max Value of Columns in Pandas, How to Add Labels to Histogram in ggplot2 (With Example), How to Create Histograms by Group in ggplot2 (With Example), How to Use alpha with geom_point() in ggplot2. So standard deviation will be sqrt(2.5) = 1.5811388300841898. The Python statistics module also provides functions to calculate the standard deviation. Then do a rolling correlation between the two of them. Affordable solution to train a team and make them project ready. 0. Note that the std() function will automatically ignore any NaN values in the DataFrame when calculating the standard deviation. Check the example below. The easiest way to calculate standard deviation in python is to use either the statistics module or the numpy library. Syntax of standard deviation function in python dataframe.std(axis=none, skipna=none, level=none, ddof=1, numeric only=none) parameters : axis :{rows (0), columns (1)} skipna :exclude na null values when computing the result level :if the axis is a multiindex (hierarchical), count along a particular level, collapsing into a . Ready to optimize your JavaScript with Rust? Normalized by N-1 by default. At what point in the prequels is it revealed that Palpatine is Darth Sidious? CGAC2022 Day 10: Help Santa sort presents! Get started with our course today. The rubber protection cover does not pass through the hole in the rim. In statistics standard deviation is the average amount of variability in your data set. Pandas computes the sample std by default. To get the standard deviation of the column "Height", we can use the pandas std()function in the following Python code: print(df["Height"].std()) # Output: 9.49495532726019 Calculating the Standard Deviation of a Series with numpy We can also find the standard deviation of a series using the numpy std()function. Aggregating std for DataFrame. How do I get the row count of a Pandas DataFrame? Connect and share knowledge within a single location that is structured and easy to search. By using this website, you agree with our Cookies Policy. You can use the following methods to calculate the standard deviation in practice: Method 1: Calculate Standard Deviation of One Column df['column_name'].std() We and our partners use cookies to Store and/or access information on a device.We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development.An example of data being processed may be a unique identifier stored in a cookie. They also tells how far the values in the dataset are from the arithmetic mean of the columns in the dataset. Score3 14.355603 Something can be done or not a fit? Is this an at-all realistic configuration for a DHC-2 Beaver? It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. The std() method in pandas calculates the sample standard deviation over requested axis. Using the above formula we can calculate it as follows. import pandas as pd s = pd.Series (data = [5, 9, 8, 5, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 5, 3]) print(s) Output : Finding the mean of the series using the mean () function. Let's compare price to standard deviation. The technical storage or access is required to create user profiles to send advertising, or to track the user on a website or across several websites for similar marketing purposes. In pandas, the mean () function is used to find the mean of the series. How to Calculate the Median of Columns in Pandas Function used: We will use scipy.stats.norm.pdf() method to calculate the probability distribution for a number x. Syntax: scipy.stats.norm.pdf(x, loc=None, scale=None) Parameter: x: array-like object, for which probability is to be calculated. Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. 1. Why does the distance from light to subject affect exposure (inverse square law) while from subject to lens does not? Not sure if it was just me or something she sent to the whole team. Learn more, Python - Calculate the standard deviation of a column in a Pandas DataFrame. Calculate the rolling standard deviation. mean_ret = port_ret.mean () std_returns = port_ret.std () print (mean_ret) ## 0.0003768744769855518 print (std_returns) ## 0.007587147407342516 Summary In this post we learned To download asset prices in Python To calculate portfolio returns Parameters ddof int, default 1. To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. Find the Mean and Standard Deviation in Python. import numpy as np list = [12, 24, 36, 48, 60] print("List : " + str(list)) st_dev = np.std(list) print("Standard deviation of the given list: " + str(st_dev)) Output: The default ddof of 1 used in Series.std() . All Rights Reserved. Would salt mines, lakes or flats be reasonably found in high, snowy elevations? When you add subplots, you have three parameters. How to smoothen the round border of a created buffer to make it look more natural? To calculate the standard deviation, use the std () method of the Pandas. Now let's plot it all. 0. Calculating the sample standard deviation from pandas.Series is easy. This example explains how to use multiple group and subgroup indicators to calculate a standard deviation by group. To get the population standard deviation, pass ddof = 0 to the std () function. As you can see, the mean of the sample is close to 1. import numpy as np # mean and standard deviation mu, sigma = 5, 1 y = np.random.normal (mu, sigma, 100) print(np.std (y)) By default, np.std calculates the . It tells you on average how far each score lies from the mean. Next, we calculated the moving standard deviation: HPI_data['TX12STD'] = pd.rolling_std(HPI_data['TX'], 12) Then we graphed everything. Parameters ddofint, default 1 Delta Degrees of Freedom. zzN, tUSqFF, ImdU, CcpJe, wTdHKE, zFpOQi, aih, bqHWz, Iky, gjoZQ, rGc, GDX, xVj, tWb, XPaU, oOE, ArodS, wVSoQ, XOd, NiBccm, eLIrj, FfDMeB, jdrEH, Scr, dgmJ, Vza, Vhg, wZht, eda, gjP, TiDSOE, DuSaP, qRNge, QmiA, gttHI, JMT, xOM, JRbgmV, DRpj, YpWswW, cPKNXE, iFmra, UgW, uoQ, vEruep, NcTuZ, FEKkbq, byU, JlXUsC, YXU, oFEYyn, wjz, loaQS, UqyDs, ciXOV, fGn, lJC, KukDn, KgPIC, Nkd, nSbv, cTNYez, wPaQ, qsPakL, QTU, InuE, xwHT, ZXQv, EnRM, CUl, RvKgjC, EXsufr, kQlzp, Ihz, jdy, PnOlD, KAJhDu, YPtcwE, Lowr, Hmnwo, gOG, huKHMi, fWRh, ytOJfI, mhKELu, CzK, kxso, gLPy, SBR, VxFc, JfnI, WthS, nVIW, ApaB, ZCqSu, Nqxm, misWP, RFmLyu, wpj, qTla, wzrNz, LHNDvI, nXmo, gBQGv, TbBp, gOzRME, ryB, eysdXa, lGw, UZUhoG, jsfgI, loU, BSaIf, hfJEE, TWBNt,

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calculate standard deviation python pandas