Summary Statistics with Python
Summary statistics gives you the tools you need to boil down massive datasets to reveal the highlights. In this chapter, you'll explore summary statistics including mean, median, and standard deviation, and learn how to accurately interpret them. You'll also develop your critical thinking skills, allowing you to choose the best summary statistics for your data. This is the Summary of lecture "Introduction to Statistics in Python", via datacamp.
- What is statistics?
- Measures of center
- Measures of spread
import numpy as np import pandas as pd import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = (10, 8)
What is statistics?
- the practice and study of collecting and analyzing data
- Summary Statistic - A fact about or summary of some data
- How likely is someone to purchase a product? Are people more likely to purchase it if they can use a different payment system?
- How many occupants will your hotel have? How can you optimize occupancy?
- How many sizes of jeans need to be manufactured so they can fit 95% of the population? Should the same number of each size be produced?
- A/B tests: Which ad is more effective in getting people to purchase product?
- Type of statistics
- Descriptive statistics
- Describe and summarize data
- Inferential statistics
- Use a sample of data to make inferences about a larger population
- Descriptive statistics
- Type of data
- Numeric (Quantitative)
- Continuous (Measured)
- Discrete (Counted)
- Categorical (Qualitative)
- Nomial (Unordered)
- Ordinal (Ordered)
- Numeric (Quantitative)
Mean and median
In this chapter, you'll be working with the 2018 Food Carbon Footprint Index from nu3. The
food_consumption dataset contains information about the kilograms of food consumed per person per year in each country in each food category (
consumption) as well as information about the carbon footprint of that food category (
co2_emissions) measured in kilograms of carbon dioxide, or $CO_2$, per person per year in each country.
In this exercise, you'll compute measures of center to compare food consumption in the US and Belgium.
food_consumption = pd.read_csv('./dataset/food_consumption.csv', index_col=0) food_consumption.head()
be_consumption = food_consumption[food_consumption['country'] == 'Belgium'] # Filter for USA usa_consumption = food_consumption[food_consumption['country'] == 'USA'] # Calculate mean and median consumption in Belgium print(np.mean(be_consumption['consumption'])) print(np.median(be_consumption['consumption'])) # Calculate mean and median consumption of USA print(np.mean(usa_consumption['consumption'])) print(np.median(usa_consumption['consumption']))
42.132727272727266 12.59 44.650000000000006 14.58
be_and_usa = food_consumption[(food_consumption['country'] == 'Belgium') | (food_consumption['country'] == 'USA')] # Group by country, select consumption column, and compute mean and median print(be_and_usa.groupby('country')['consumption'].agg([np.mean, np.median]))
mean median country Belgium 42.132727 12.59 USA 44.650000 14.58
Mean vs. median
In the video, you learned that the mean is the sum of all the data points divided by the total number of data points, and the median is the middle value of the dataset where 50% of the data is less than the median, and 50% of the data is greater than the median. In this exercise, you'll compare these two measures of center.
rice_consumption = food_consumption[food_consumption['food_category'] == 'rice'] # Histogram of co2_emission for rice and show plot rice_consumption['co2_emission'].hist(); # Calculate mean and median of co2_emission with .agg() print(rice_consumption['co2_emission'].agg([np.mean, np.median]))
mean 37.591615 median 15.200000 Name: co2_emission, dtype: float64
Measures of spread
- Average distance from each data point to the data's mean
- Standard deviation
- Mean absolute deviation
- Standard deviation vs. mean absolute deviation
- Standard deviation squares distances, penalizing longer distances more than shorter ones
- Mean absolute deviation penalizes each distance equally
- Quantiles (Or percentiles)
- Interquartile range (IQR)
- Height of the box in a boxplot
- Data point that is substantially different from the others
Quartiles, quantiles, and quintiles
Quantiles are a great way of summarizing numerical data since they can be used to measure center and spread, as well as to get a sense of where a data point stands in relation to the rest of the data set. For example, you might want to give a discount to the 10% most active users on a website.
In this exercise, you'll calculate quartiles, quintiles, and deciles, which split up a dataset into 4, 5, and 10 pieces, respectively.
print(np.quantile(food_consumption['co2_emission'], np.linspace(0, 1, 5))) # Calculate the quintiles of co2_emission print(np.quantile(food_consumption['co2_emission'], np.linspace(0, 1, 6))) # Calculate the deciles of co2_emission print(np.quantile(food_consumption['co2_emission'], np.linspace(0, 1, 10)))
[ 0. 5.21 16.53 62.5975 1712. ] [ 0. 3.54 11.026 25.59 99.978 1712. ] [0.00000000e+00 9.05555556e-01 4.19111111e+00 8.05333333e+00 1.32000000e+01 2.10944444e+01 3.58666667e+01 7.90622222e+01 1.86115556e+02 1.71200000e+03]
Variance and standard deviation
Variance and standard deviation are two of the most common ways to measure the spread of a variable, and you'll practice calculating these in this exercise. Spread is important since it can help inform expectations. For example, if a salesperson sells a mean of 20 products a day, but has a standard deviation of 10 products, there will probably be days where they sell 40 products, but also days where they only sell one or two. Information like this is important, especially when making predictions.
print(food_consumption.groupby('food_category')['co2_emission'].agg([np.var, np.std])) # Create histogram of co2_emission for food_category 'beef' food_consumption[food_consumption['food_category'] == 'beef']['co2_emission'].hist();
var std food_category beef 88748.408132 297.906710 dairy 17671.891985 132.935669 eggs 21.371819 4.622966 fish 921.637349 30.358481 lamb_goat 16475.518363 128.356996 nuts 35.639652 5.969895 pork 3094.963537 55.632396 poultry 245.026801 15.653332 rice 2281.376243 47.763754 soybeans 0.879882 0.938020 wheat 71.023937 8.427570
food_consumption[food_consumption['food_category'] == 'eggs']['co2_emission'].hist();
Finding outliers using IQR
Outliers can have big effects on statistics like mean, as well as statistics that rely on the mean, such as variance and standard deviation. Interquartile range, or IQR, is another way of measuring spread that's less influenced by outliers. IQR is also often used to find outliers. If a value is less than $Q1−1.5×IQR$ or greater than $Q3+1.5×IQR$, it's considered an outlier. In this exercise, you'll calculate IQR and use it to find some outliers.
emissions_by_country = food_consumption.groupby('country')['co2_emission'].sum() print(emissions_by_country)
country Albania 1777.85 Algeria 707.88 Angola 412.99 Argentina 2172.40 Armenia 1109.93 ... Uruguay 1634.91 Venezuela 1104.10 Vietnam 641.51 Zambia 225.30 Zimbabwe 350.33 Name: co2_emission, Length: 130, dtype: float64
q1 = np.quantile(emissions_by_country, 0.25) q3 = np.quantile(emissions_by_country, 0.75) iqr = q3 - q1 # Calculate the lower and upper cutoffs for outliers lower = q1 - 1.5 * iqr upper = q3 + 1.5 * iqr # Subset emissions_by_country to find outliers outliers = emissions_by_country[(emissions_by_country > upper) | (emissions_by_country < lower)] print(outliers)
country Argentina 2172.4 Name: co2_emission, dtype: float64