Let's Talk About Statistics - Introduction to Statistics for Software Quality (No.7: Introduction to Statistical Graphs with Python and Excel)

In the seventh installment of "Let's Talk About Statistics," we introduce how to create practical graphs for real-world use.

Concepts introduced so far—such as “measures of central tendency,” “variability,” and “distribution shape”—are most valuable when presented visually.
This time, we'll actually draw the following statistical graphs—commonly used in the field—using both Python (matplotlib/pandas) and Excel.
For the Python examples, we've added brief explanations; for Excel, we've outlined simple steps for creating each chart. Please try them out yourself!

• Bar Chart: Ideal for comparing quantities across categories
• Line Chart: Effective for capturing time-series changes and trends
• Scatter Plot: Visualize the relationship between two numerical variables
• Histogram: Understand the distribution shape of continuous data
• Box Plot: Perfect for visualizing variability, skew, and outliers
• Pareto Chart: Useful for determining priority areas and setting priorities

In this section, we'll set up the environment needed to plot statistical graphs with Python.
No special development environment is required; it's assumed that Python is running on your local PC.

• Python 3.9 or above (recommended)

The following libraries are used. Install them by running:

pip install matplotlib pandas numpy

• matplotlib: Fundamental library for plotting graphs
• pandas: Convenient for DataFrame operations
• numpy: Used for data generation and statistical calculations

To prevent garbled Japanese text, specify the font in matplotlib settings:

import matplotlib.pyplot as plt
plt.rcParams['font.family'] = 'Meiryo'  # Use 'Meiryo' for Windows, 'AppleGothic' for macOS

Jupyter Lab allows you to run code interactively in your browser, making it ideal for checking graphs as you go.
Install with:

pip install jupyterlab

Start with:

jupyter lab

We'll use Microsoft 365's Excel.
Installation details for Excel are omitted.

Bar charts are extremely effective for visually grasping the differences in quantities across categories.
In software quality management, they shine for use cases such as “number of occurrences by bug type” or “comparison of review issue counts.”

Assume the following bug count data by category:

import matplotlib.pyplot as plt

plt.rcParams['font.family'] = 'Meiryo'

categories = ["UI", "ロジック", "性能", "その他"]
counts = [10, 15, 8, 5]

plt.bar(categories, counts, color='salmon', edgecolor='black')
plt.title("バグ種別の件数")
plt.xlabel("カテゴリ")
plt.ylabel("件数")
plt.tight_layout()
plt.show()

Explanation (Python)

• plt.bar() draws the bar chart.
• color='salmon' sets the bar color, and edgecolor='black' clarifies the edges.
• Using tight_layout() prevents label overlap and makes the chart more readable.
• We use plt.rcParams['font.family'] = 'Meiryo' to display Japanese text (for Windows environments).

1. Enter categories in column A and bug counts in column B.
2. Select the range, then choose Insert → Chart → Column Chart.
3. (Optional) Set the chart title and axis labels.

Explanation (Excel)

• In Excel, you can easily visualize quantities by category using a Column Chart.
• The horizontal axis displays “Category,” and the vertical axis displays “Count.”
• Bar charts are ideal when the data is categorical (nominal scale).

• Bar charts are excellent for comparing values.
• However, for time-series data (e.g., monthly changes), a line chart is the standard choice. Choosing appropriately is important.

Line charts are suitable for grasping changes and trends over time.
By connecting data points recorded at regular intervals (daily, weekly, monthly, etc.) with lines, you can visualize trends.
In quality management, they are widely used for progress tracking, anomaly detection, and verifying improvement effects.

Assume the following daily bug count data:

import matplotlib.pyplot as plt

plt.rcParams['font.family'] = 'Meiryo'

days = ["月", "火", "水", "木", "金"]
bugs = [5, 3, 6, 4, 2]
plt.plot(days, bugs, marker='o')
plt.title("日別バグ件数")
plt.xlabel("曜日")
plt.ylabel("件数")
plt.tight_layout()
plt.show()

Explanation (Python)

• plt.plot() is used to draw the line chart.
• Specifying marker='o' displays each data point as a circle.
• plt.tight_layout() ensures that chart elements do not get cut off.

1. Enter days in column A and bug counts in column B.
2. Select the range, then choose Insert → Chart → Line Chart.
3. (Optional) Set the chart title and axis labels.

Explanation (Excel)

• With just two columns of data (day and count), inserting a line chart is simple.
• Excel automatically interprets the X-axis as a categorical axis.
• Adding axis titles or data labels can make the chart even clearer.

• The horizontal axis uses the ordered “days of the week,” making lines appropriate.
• Line charts are great for showing “flow” or “trends,” but are not suitable when categories have no inherent order (e.g., names of team members).
• If there are too few data points, the line may be overemphasized, leading to misinterpretation of trends.

Scatter plots are ideal for visualizing the relationship (correlation) between two numerical variables.
In software quality, they can help uncover links such as review time vs. number of issues or number of test cases vs. bug count.

Assume the following review time vs. issue count data:

import matplotlib.pyplot as plt

plt.rcParams['font.family'] = 'Meiryo'

x = [10, 20, 30, 40, 50]  # Review time
y = [2, 3, 4, 8, 15]      # Number of issues

plt.scatter(x, y, color='dodgerblue', edgecolor='black')
plt.title("レビュー時間と指摘数の関係")
plt.xlabel("レビュー時間（分）")
plt.ylabel("指摘数")
plt.grid(True)
plt.tight_layout()
plt.show()

Explanation (Python)

• plt.scatter() plots the scatter points.
• You can customize point color and edgecolor.
• Enabling grid(True) adds grid lines, which make the relationships easier to read.
• Adding a regression line (Note 1) lets you assess the strength and direction of the trend.

1. Enter “Review Time (min)” in column A and “Number of Issues” in column B.
2. Select the range, then choose Insert → Chart → Scatter (points).
3. Add a trendline (regression line) if needed.

Explanation (Excel)

• Excel’s scatter plot automatically sets “Review Time” on the X-axis and “Number of Issues” on the Y-axis.
• Right-click the data points and choose “Add Trendline” to display a regression line.
• If points overlap, adjusting point size or transparency can improve visibility.

• Scatter plots are for numerical relationships, so they’re unsuitable for categorical data.
• If points overlap too much, use alpha (transparency) or jitter (small random offsets) to improve clarity.
• Highlighting outliers or adding a trendline can deepen your analysis.

Histograms are suitable for visually grasping the distribution shape of continuous data.
They are essential for understanding variability in quantitative data such as bug fix times or test execution durations.

Assume the following test execution times (minutes) for 30 runs:

import matplotlib.pyplot as plt

plt.rcParams['font.family'] = 'Meiryo'

# Test execution time data (unit: minutes)
test_times = [
    12, 15, 18, 20, 22, 23, 25, 25, 26, 28,
    29, 30, 30, 31, 32, 33, 34, 35, 36, 38,
    39, 40, 42, 43, 45, 47, 49, 50, 52, 55
]

# Draw the histogram
plt.figure(figsize=(8, 5))
plt.hist(test_times, bins=8, edgecolor='black')
plt.title('テスト実行時間の分布（単位：分）')
plt.xlabel('テスト実行時間（分）')
plt.ylabel('件数')
plt.grid(True, linestyle='--', alpha=0.5)
plt.tight_layout()
plt.show()

Explanation (Python)

• plt.hist() is used to draw the histogram.
• bins=8 specifies the number of bins; adjusting this value changes the readability.
• edgecolor='black' clarifies the bar edges and improves readability.

1. Prepare the execution time data in column A.
2. Select the range, then choose Insert → Statistical Chart → Histogram.
3. Adjust the number of bins and labels to improve readability.

Explanation (Excel)

• Excel automatically calculates bins for histograms.
• In [Axis Options], you can manually adjust [Bin width] or [Number of bins].
• If there are many outliers, consider techniques such as using a log scale.

• Bin settings (number and width) greatly affect the chart’s appearance.
• Avoid judging solely by looks; be mindful of the underlying statistical properties.
• If outliers stand out, adding annotations can be more considerate.

Box plots are a powerful way to visualize data spread, skewness, and outliers at a glance.
Based on quartiles, they simultaneously show the median, interquartile range (IQR), minimum, maximum, and outliers.

Assume the following review time data (minutes):

import matplotlib.pyplot as plt

plt.rcParams['font.family'] = 'Meiryo'

data = [19, 20, 21, 21, 22, 23, 24, 25, 26, 27, 55]
plt.boxplot(data, vert=False, patch_artist=True)
plt.title("レビュー時間のばらつき")
plt.xlabel("時間（分）")
plt.tight_layout()
plt.show()

Explanation (Python)

• plt.boxplot() is the function for drawing a box plot.
• Setting patch_artist=True allows the box to be filled with color.
• Specifying vert=False makes the box plot horizontal.
• Outliers (e.g., 55) are automatically shown as points outside the whiskers.

1. Enter the data in column A.
2. Select the range, then choose Insert → Statistical Chart → Box Plot.
3. Adjust the title and axes as needed.

Explanation (Excel)

• In Excel, you can easily insert a box plot as a statistical chart.
• If there are outliers, they are automatically displayed as circles.
• The interquartile range (IQR) and median can also be visually confirmed.

• When outliers are extreme, the scale can be distorted, so caution is needed.
• When comparing multiple groups side by side, their scales must be unified.
• For small datasets, the box may appear very small, so adding additional explanations can be helpful.

Pareto charts combine a bar chart and a line chart to visualize counts by factor alongside their cumulative percentage.
They help you apply the “vital few vs. trivial many (80:20 rule)” concept and are ideal for allocating resources and prioritizing improvements.

Assume the following bug type count data:

import matplotlib.pyplot as plt
import numpy as np

plt.rcParams['font.family'] = 'Meiryo'

labels = ["ロジック", "UI", "性能", "テスト漏れ", "その他"]
values = [18, 12, 9, 6, 5]

# Calculate cumulative percentage
cum_values = np.cumsum(values)
total = sum(values)
cum_percentage = cum_values / total * 100

fig, ax1 = plt.subplots()

# Bar chart (counts)
ax1.bar(labels, values, color='skyblue', edgecolor='black')
ax1.set_ylabel('件数', color='black')
ax1.tick_params(axis='y', labelcolor='black')

# Line chart (cumulative percentage)
ax2 = ax1.twinx()
ax2.plot(labels, cum_percentage, color='red', marker='o')
ax2.set_ylabel('累積比率（％）', color='red')
ax2.tick_params(axis='y', labelcolor='red')
ax2.set_ylim(0, 100)

plt.title('バグ種別ごとの件数と累積比率（パレート図）')
plt.grid(True, axis='y', linestyle='--', alpha=0.5)
plt.tight_layout()
plt.show()

Explanation (Python)

• bar() draws counts by category, and plot() overlays the cumulative percentage as a line.
• twinx() allows sharing different Y-axes for the bar and line charts.
• np.cumsum() computes cumulative sums and percentages.

1. Enter bug types in column A and counts in column B.
2. Sort the data in descending order of count.
3. Add a cumulative percentage column (cumulative sum ÷ total).
4. Insert a combo chart combining a column chart and a line chart.

Explanation (Excel)

• Since the bar and line use different axes, be sure to set axis labels.
• The items must be sorted in descending order of count for a meaningful Pareto chart.
• In Excel, selecting “Combo Chart” lets you combine a bar chart and a line chart.

• It is essential to sort categories in descending order.
• Always display the cumulative percentage on the secondary axis.
• Items not in the top 20% may still be important, so exercise caution.

• Always include a title, axis labels, and legend on your charts.
• Adding annotations can be effective when there are outliers or noticeable trends.
• For internal documents, it’s helpful to provide explanatory text alongside the chart.

• With Python or Excel, anyone can create statistical charts.
• Meaningful charts support both analysis and communication.
• Master the basics and choose the format that fits your purpose.

Next time: “Intuition and Calculation of Probability: Understanding the Nature of ‘Chance’.”
We’ll explain the basics of probability—deeply related to statistics—in an intuitive and practical way.

I've compiled statistical resources here.
I hope you find them useful for your data analysis.