Probability and statistics are essential tools for chemical engineers working in Kenya’s dynamic industries. These disciplines enable engineers to analyse experimental data, assess process variability, and make informed decisions under uncertainty, such as optimizing chemical reactions or ensuring safety in production plants. Understanding data classification, presentation, and measures of central tendency and dispersion supports robust process control and quality assurance in chemical manufacturing.

10.1 Classification of Data

Classification of data is the foundation of statistical analysis in chemical engineering. It involves organizing raw data into meaningful categories to simplify interpretation and further analysis. Chemical engineers collect data from experiments and industrial processes that must be classified correctly to identify trends, variability, and potential issues in process performance.

10.1.1 Types of Data

Data can be classified into two main types: qualitative and quantitative.

• Qualitative data represent non-numeric categories or attributes, such as types of chemical reactions or equipment status (operational/faulty).
• Quantitative data are numeric and measurable, such as temperature, pressure, or concentration.
• Quantitative data further divide into discrete data (countable values, e.g., number of defective products) and continuous data (measurable values within a range, e.g., flow rate).
• Correctly identifying data type determines the appropriate statistical tools and graphical methods.
• For example, a chemical plant monitoring batch yields records yield amounts (quantitative continuous), while recording batch types is qualitative.

10.1.2 Data Collection

Data collection in chemical engineering involves systematic measurement and recording of process variables or experimental results.

• Step 1: Define the objective of data collection, such as monitoring catalyst activity.
• Step 2: Identify relevant variables and measurement methods (e.g., sensors, manual sampling).
• Step 3: Select sampling techniques: random sampling to avoid bias, or systematic sampling for consistency.
• Step 4: Record data accurately with units and time stamps.
• Step 5: Verify data integrity by cross-checking and validating measurements.
• Step 6: Store data securely for analysis and future reference.

10.1.3 Tabulation of Data

Tabulation organizes raw data into tables for clarity and ease of analysis.

• Data are grouped into classes or categories with corresponding frequencies.
• Frequency tables display the number of observations in each class.
• Class intervals define ranges for grouped data, for example, temperature ranges of 50-60°C.
• Cumulative frequency tables show the total frequency up to a class interval.
• Proper tabulation aids visualisation and calculation of statistical measures.

Worked Example

Example: A chemical plant records the following temperatures (°C) from 10 batches: 52, 55, 58, 60, 54, 57, 59, 53, 56, 61. Group the data into class intervals of 52-54, 55-57, 58-60, 61-63 and construct a frequency and cumulative frequency table.

Step 1: Assign each value to a class interval:

• 52, 53, 54 → 52-54
• 55, 56, 57 → 55-57
• 58, 59, 60 → 58-60
• 61 → 61-63

Step 2: Count frequencies:
| Class Interval (°C) | Frequency |
|---|---|
| 52-54 | 3 |
| 55-57 | 3 |
| 58-60 | 3 |
| 61-63 | 1 |

Step 3: Calculate cumulative frequencies:
| Class Interval (°C) | Frequency | Cumulative Frequency |
|---|---|---|
| 52-54 | 3 | 3 |
| 55-57 | 3 | 6 |
| 58-60 | 3 | 9 |
| 61-63 | 1 | 10 |

Answer: Frequency and cumulative frequency tables constructed.

10.1.4 Diagrammatic and Graphical Presentation of Data

Graphical methods enable chemical engineers to visualize data patterns and distributions quickly.

• Histograms represent frequency distribution of grouped data with adjacent bars.
• Frequency polygons connect midpoints of histogram bars with lines, showing trends.
• Bar charts compare frequencies or quantities across categories.
• Pie charts display proportional data as slices of a circle.
• Cumulative frequency curves (ogives) depict running totals and help find medians and percentiles.
• Selecting the correct graphical method depends on data type and analysis goals.

Worked Example

Example: The following defect counts were recorded in 5 batches at Bamburi Cement: 2, 4, 3, 5, 3. Construct a bar chart and a frequency polygon.

Step 1: Tabulate frequencies:
| Defect Count | Frequency |
|---|---|
| 2 | 1 |
| 3 | 2 |
| 4 | 1 |
| 5 | 1 |

Step 2: Bar Chart

• Draw x-axis with defect counts (2, 3, 4, 5).
• Draw y-axis with frequency.
• Draw bars for each defect count according to frequency.

Step 3: Frequency Polygon

• Plot points at (2,1), (3,2), (4,1), (5,1).
• Connect points with straight lines.

Answer: Bar chart and frequency polygon constructed for defect count data.

Chapter Summary

This chapter begins by exploring the classification of data into grouped and ungrouped forms, emphasizing the importance of proper data collection methods. It then covers the tabulation of data, including the construction of frequency tables with class intervals and class boundaries to organize information effectively. Various diagrammatic and graphical presentations of data are explained, such as histograms, frequency polygons, bar charts, pie charts, and cumulative frequency curves, which help visualize data distributions clearly. The chapter proceeds to discuss measures of central tendency, focusing on mean, mode, and median as key indicators of data centrality. Finally, it introduces measures of dispersion, which describe the variability within data sets, enabling a comprehensive understanding of data behavior in engineering contexts. Together, these topics provide essential tools for analyzing and interpreting statistical data in engineering practice.