ECON 0150 | Economic Data Analysis

The economist’s data analysis skillset.


Part 1.2 | Cross-Sectional (Numerical) Data

Cross-Sectional Numerical Data

Comparing numerical values across entities

> Cross-sectional data: many entities, one point in time

> Numerical variables: values you can do math with (age, income, consumption)

> Key question: How is this variable distributed?

Two Tools for Numerical Distributions

Choose based on sample size and what you want to see

Tool Best for Shows
Histogram Many observations Shape of distribution
Boxplot + Stripplot Fewer observations Quartiles + individual values

Histograms: Shape of the Distribution

Use when you have many observations

Histograms

Q. Which age group has the most Starbucks customers?

> the bin sizes aren’t even, making it hard to interpret

Numerical Variables: Histograms

Q. Which age group has the most Starbucks customers?

> the bin sizes aren’t even, making it hard to interpret

Histograms: Use equal sized bins

Q. Which age group has the most Starbucks customers?

> but what if we want to distinguish between a 55 year old and a 60 year old?

Histograms: Use narrow enough bins

Q. Which age group has the most Starbucks customers?

> what if we take this even further?

> what if we compare 44 year olds to 45 year olds?

Histograms: Avoid visualizing noise

Q. Do 44 or 45 year olds spend more at Starbucks?

> we can go too far, introducing statistical noise. how do we fix the problem?

> increase the sample size or the bin width!

Histograms: Balance resolution vs noise

Q. Which age group has the most Starbucks customers?

> larger sample has less noise!

Histograms: Balance resolution vs noise

Q. Which age group has the most Starbucks customers?

> larger bins also has less noise!

Describing the Distribution: Center and Spread

Two numbers that summarize a histogram

  • Mean — the average value (center)
  • Standard Deviation (SD) — typical distance from the mean (spread)

Mean and Standard Deviation

Q. What is the average age of Starbucks customers?

> Mean ≈ 56 years; SD ≈ 17 years

> “The average customer is about 56; ages typically vary by about 17 years from that average”

Histograms: Summary

… use the right summary tool for the variable type



  • Use histograms to visualize continuous variables.
  • Make histograms with equally sized bins.
  • Histograms with bins that are too narrow increase statistical noise, which can obscure underlying relationships.

S-T-E for Histograms

What we just did

Step Action
SELECT All Starbucks customers
TRANSFORM Count customers within each age bin
ENCODE Bin → x-position; Count → bar height

> TRANSFORM for histograms = count within bins

Exercise 1.2 | Histograms

Q. Which age group among those making $40k or less has the most Starbucks customers?



Lets use the data to examine whether customers between 45 - 55 years old spend the most among customers making less than $40k.

Data: Starbucks_Customer_Profiles_40k.csv

Exercise 1.2 | Histograms

Q. Which age group among those making $40k or less has the most Starbucks customers? 

# Histogram with 5 year bins
sns.histplot(customers, x='age', bins=range(20,100,5))

# Save Figure
plt.savefig('exercise_1_2_histogram.png')

Exercise 1.2 | Mean and Standard Deviation

Summarize the distribution with two numbers 

# Calculate the mean
customers['age'].mean()
# Calculate the standard deviation
customers['age'].std()

> Mean tells us the center; SD tells us the spread


“The average customer is about 48 years old; ages typically vary by about 18 years from that average.”

What if we have fewer observations?

Histograms need many data points to show shape

> With few observations, histogram bins become noisy or empty

> We need a different tool: boxplots + stripplots

Histograms vs Boxplots

Q. Which countries drank an average amount of coffee?

> histogram bins make it impossible to see exact values or quartiles

Boxplots

Q. Which countries drank the most coffee in 1999?

> as we’ll see, boxplots can tell us about quartiles

> but boxplots are still pretty unclear for our question

Boxplots + Stripplots

Q. Which countries drank the most coffee in 1999?

> here we can see the datapoints directly with the boxplot

> each point represents a country’s coffee consumption

Boxplots + Stripplots

Q. Which countries drank the most coffee in 1999?

> each element of the boxplot represents one of these five quartiles

Boxplots + Stripplots

Which countries consumed more than 8 kg per capita?

Boxplots + Stripplots

Which countries consumed more than 8 kg per capita?

> we can highlight the relevant subsets of the data

Boxplots + Stripplots

Which country consumed the most coffee per capita?

> we can find the exact values according to quartiles

Boxplots + Stripplots

Which country consumed the most coffee per capita?

> we can find the exact values according to quartiles

> Finland consumed the most coffee per capita in 1999

Boxplots + Stripplots

Which country consumed the least coffee per capita?

Boxplots + Stripplots

Which country consumed the least coffee per capita?

> Russia consumed the least coffee per capita in 1999

Boxplots + Stripplots

How about the median?

Boxplots + Stripplots

How about the median?

> the US!

Boxplots + Stripplots

Which country consumes more than exactly 25% of countries?

Boxplots + Stripplots

Which country consumes more than exactly 25% of countries?

> Slovakia!

Boxplots + Stripplots

Which country consumes more than exactly 75% of countries?

Boxplots + Stripplots

Which country consumes more than exactly 75% of countries?

> Netherlands

Boxplots + Stripplots

Boxplots show quartiles; stripplots show the data.

Boxplots + Stripplots: Summary

Boxplots show quartiles; stripplots show the data.



  • Boxplots make it easy to show the quartiles.
  • Stripplots can show the distribution of the data.
  • We can highlight subsets of the data.

S-T-E for Boxplots + Stripplots

What we just did

Step Action
SELECT All coffee-importing countries in 1999
TRANSFORM Calculate quartiles (min, Q1, median, Q3, max)
ENCODE Quartile → box position; Value → point position

> TRANSFORM for boxplots = calculate quartiles

Exercise 1.2 | Boxplots + Stripplots

Show the distribution of coffee consumption per capita in 2019.



Lets use a boxplot and stripplot to examine the distribution of coffee consumption per capita among coffee-importing countries in 2019.

  • Data: Coffee_Per_Cap_2019.csv

Exercise 1.2 | Boxplots + Stripplots

Show the distribution of coffee consumption per capita in 2019. 

# Boxplot with no outliers
sns.boxplot(coffee, x='Coffee_2019', whis=(0,100))
# Stripplot
sns.stripplot(coffee, x='Coffee_2019')

# Save Figure
plt.savefig('exercise_1_2_boxplot.png')

Exercise 1.2 | Quartiles

Calculate the five-number summary 

# Minimum and Maximum
coffee['Coffee_2019'].min()
coffee['Coffee_2019'].max()
# Quartiles (Q1, Median, Q3)
coffee['Coffee_2019'].quantile(0.25)
coffee['Coffee_2019'].median()
coffee['Coffee_2019'].quantile(0.75)

> These five numbers define the boxplot: min, Q1, median, Q3, max

Building Blocks

What this unit adds to your toolkit

Block New in 1.2
Variables Numerical
Structures Cross-section
Operations Bin, Mean, SD, Quartiles
Visualizations Histogram, Boxplot, Stripplot


> Next: lets add a time dimension