Histograms in Data Analysis Python - Step-by-Step Execution

Concept Flow - Histograms

Start with data array

↓

Divide data into bins

↓

Count data points in each bin

↓

Draw bars with heights = counts

↓

Display histogram plot

↓

End

We start with data, split it into groups called bins, count how many points fall in each bin, then draw bars showing these counts.

Execution Sample

Data Analysis Python

import matplotlib.pyplot as plt
import numpy as np
data = np.array([1,2,2,3,3,3,4,4,5])
plt.hist(data, bins=4)
plt.show()

This code creates a histogram of the data array with 4 bins and shows the plot.

Execution Table

Step	Action	Data State	Bins	Bin Counts	Plot Bars Height
1	Start with data array	[1,2,2,3,3,3,4,4,5]	Not set	Not counted	No bars
2	Divide data into 4 bins	Same data	[1.0-2.0), [2.0-3.0), [3.0-4.0), [4.0-5.0]	Not counted	No bars
3	Count points in each bin	Same data	Same bins	[1, 2, 3, 3]	No bars yet
4	Draw bars with heights = counts	Same data	Same bins	Same counts	[1, 2, 3, 3] heights
5	Display histogram plot	Same data	Same bins	Same counts	Bars visible with heights 1,2,3,3

💡 Histogram displayed with bars representing counts in each bin.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	Final
data	[1,2,2,3,3,3,4,4,5]	[1,2,2,3,3,3,4,4,5]	[1,2,2,3,3,3,4,4,5]	[1,2,2,3,3,3,4,4,5]	[1,2,2,3,3,3,4,4,5]
bins	Not set	[1.0-2.0), [2.0-3.0), [3.0-4.0), [4.0-5.0]	[1.0-2.0), [2.0-3.0), [3.0-4.0), [4.0-5.0]	[1.0-2.0), [2.0-3.0), [3.0-4.0), [4.0-5.0]	[1.0-2.0), [2.0-3.0), [3.0-4.0), [4.0-5.0]
bin_counts	Not counted	Not counted	[1, 2, 3, 3]	[1, 2, 3, 3]	[1, 2, 3, 3]
bars_height	No bars	No bars	No bars yet	[1, 2, 3, 3]	[1, 2, 3, 3]

Key Moments - 3 Insights

Why do some bins have more counts than others?

Because more data points fall into those bin ranges, as shown in execution_table step 3 where counts are calculated.

What happens if we change the number of bins?

The data is divided differently, changing bin ranges and counts, which changes the bars heights as seen in variable_tracker for bins and bin_counts.

Why does the last bin include the highest value?

Bins include their left edge but exclude the right edge except the last bin which includes both edges, so the highest value falls into the last bin as shown in step 2 bins.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, what is the count of data points in the second bin?

A 1

B 2

C 3

D 4

💡 Hint

Check the 'Bin Counts' column at step 3 in the execution_table.

At which step do the bars first get their heights set?

A Step 4

B Step 3

C Step 2

D Step 5

💡 Hint

Look at the 'Plot Bars Height' column in execution_table to see when bars get heights.

If we increase bins from 4 to 6, what will happen to bin_counts?

A Counts will stay the same

B Counts will all increase

C Counts will be split into more bins, likely smaller counts per bin

D Bins will merge and counts decrease

💡 Hint

Refer to key_moments about changing number of bins affecting counts.

Concept Snapshot

Histograms show data distribution by grouping values into bins.
Each bin counts how many data points fall inside.
Bars are drawn with heights equal to counts.
More bins mean finer grouping; fewer bins mean broader groups.
Use plt.hist(data, bins=n) in Python to create histograms.

Full Transcript

Histograms help us see how data spreads out. We start with a list of numbers. We split these numbers into groups called bins. Then we count how many numbers fall into each bin. These counts become the heights of bars in a bar chart. The bars show us where data is more or less common. Changing the number of bins changes how detailed the groups are. In Python, we use matplotlib's hist function to make histograms easily.

Practice

1. What does a histogram primarily show when analyzing data?

easy

A. The average value of the dataset

B. The exact values of each data point

C. The relationship between two variables

D. The frequency distribution of data values grouped into bins

Solution

1. Step 1: Understand histogram purpose

   A histogram groups data into bins and counts how many data points fall into each bin.

2. Step 2: Identify what histogram shows

   This grouping shows the frequency distribution, not exact values or relationships.

3. Final Answer:

   The frequency distribution of data values grouped into bins -> Option D

4. Quick Check:

   Histogram = frequency distribution [OK]

Hint: Histograms show counts per bin, not individual values [OK]

Common Mistakes:

• Confusing histogram with scatter plot
• Thinking histogram shows exact data points
• Assuming histogram shows averages

2. Which of the following is the correct way to create a histogram using matplotlib in Python?

easy

A. plt.plot(data)

B. plt.hist(data)

C. plt.bar(data)

D. plt.scatter(data)

Solution

1. Step 1: Recall matplotlib histogram function

   Matplotlib uses plt.hist() to create histograms from data arrays.

2. Step 2: Differentiate from other plot types

   plt.plot() is for line plots, plt.bar() for bar charts, plt.scatter() for scatter plots.

3. Final Answer:

   plt.hist(data) -> Option B

4. Quick Check:

   Histogram function = plt.hist() [OK]

Hint: Use plt.hist() to plot histograms in matplotlib [OK]

Common Mistakes:

• Using plt.plot() instead of plt.hist()
• Confusing bar chart with histogram
• Trying plt.scatter() for histograms

3. What will be the output of this code snippet?

import matplotlib.pyplot as plt
import numpy as np

data = np.array([1, 2, 2, 3, 3, 3, 4, 4, 4, 4])
plt.hist(data, bins=4)
plt.show()

medium

A. A histogram with 4 bars showing counts: 1, 2, 3, 4

B. A histogram with 4 bars showing counts: 1, 2, 3, 4 but bars are unevenly spaced

C. A histogram with 4 bars showing counts: 1, 2, 3, 4 but bars represent ranges, not exact values

D. An error because bins must be equal to the number of unique values

Solution

1. Step 1: Understand bins in histogram

   Bins divide the data range into intervals. Here, bins=4 divides data from 1 to 4 into 4 intervals.

2. Step 2: Analyze counts per bin

   Counts per bin correspond to how many data points fall into each interval, not just counts of exact values.

3. Final Answer:

   A histogram with 4 bars showing counts: 1, 2, 3, 4 but bars represent ranges, not exact values -> Option C

4. Quick Check:

   Bins = ranges, counts per range [OK]

Hint: Bins group ranges, not just unique values [OK]

Common Mistakes:

• Assuming bins equal unique values
• Thinking bars show exact counts per value
• Expecting error due to bins count

4. Identify the error in this code that tries to plot a histogram:

import matplotlib.pyplot as plt

values = [5, 7, 8, 5, 6]
plt.hist(values, bins='five')
plt.show()

medium

A. bins parameter should be an integer, not a string

B. plt.hist() does not accept lists as data

C. plt.show() is missing

D. values list must be converted to numpy array first

Solution

1. Step 1: Check bins parameter type

   bins must be an integer or sequence, not a string like 'five'.

2. Step 2: Verify other parts

   plt.hist accepts lists, plt.show() is present, numpy array conversion is optional.

3. Final Answer:

   bins parameter should be an integer, not a string -> Option A

4. Quick Check:

   bins must be int or sequence [OK]

Hint: bins must be int or list, not string [OK]

Common Mistakes:

• Passing bins as string causes error
• Thinking plt.hist needs numpy array
• Forgetting plt.show()

5. You have a dataset with ages: [22, 25, 29, 35, 40, 42, 45, 50, 55, 60]. You want to create a histogram with bins representing decades (20-29, 30-39, 40-49, 50-59, 60-69). Which bins parameter should you use in plt.hist() to get this grouping?

hard

A. [20, 30, 40, 50, 60, 70]

B. [20, 29, 39, 49, 59, 69]

C. [20, 25, 30, 35, 40, 45, 50, 55, 60, 65]

D. [21, 31, 41, 51, 61, 71]

Solution

1. Step 1: Define bin edges for decades

   Bins edges must cover ranges: 20-29, 30-39, etc. Using edges [20, 30, 40, 50, 60, 70] creates intervals [20-30), [30-40), etc.

2. Step 2: Confirm bins cover all ages

   These edges include all ages from 22 to 60 correctly in decade groups.

3. Final Answer:

   [20, 30, 40, 50, 60, 70] -> Option A

4. Quick Check:

   Bins edges = decade boundaries [OK]

Hint: Bins edges define intervals; use decade boundaries [OK]

Common Mistakes:

• Using bin edges that exclude upper bounds
• Using single values instead of edges
• Misaligning bins with decade ranges