Statistics and probability are critical tools for electrical engineering technicians in Kenya, enabling informed decision-making and effective analysis of electrical systems and data. Understanding how to summarize large datasets and measure variability ensures accuracy in quality control, fault diagnosis, and system optimization. This chapter equips learners with foundational statistical measures relevant to the electrical sector, enhancing their ability to interpret data from measurements, tests, and operational parameters reliably.

2.1 Measures of central tendency mean, mode and median

Measures of central tendency are statistical values that describe the center or typical value of a dataset. In electrical engineering contexts such as power consumption analysis or voltage measurement, these measures help summarize data sets to understand system behavior or identify anomalies. Technicians use these measures to interpret large volumes of data efficiently, aiding in troubleshooting and performance evaluation.

2.1.1 Mean: Concept and Calculation

The mean is the arithmetic average of a dataset, providing a balanced central value that accounts for every observation.

• It is calculated by summing all the numerical values and dividing by the number of observations.
• The mean is sensitive to extreme values (outliers), which can skew the average, especially in datasets with irregular measurements.
• Electrical engineers use the mean to determine average current, voltage, or power readings over time for system monitoring.
• The mean provides a simple summary measure but may not always represent the most typical value when data is skewed.
• Calculating the mean is straightforward and forms the basis for more complex statistical analysis.

Worked Example

Suppose a technician at KenGen records the following voltage readings (in volts) from a generator: 220, 225, 230, 235, 240.

Calculate the mean voltage:

• Sum all readings:$$220 + 225 + 230 + 235 + 240 = 1150$$
• Number of readings: 5
• Mean voltage:$$\text{Mean} = \frac{1150}{5} = 230 \text{ volts}$$

Answer: The mean voltage is 230 volts.

2.1.2 Median: Meaning and Application

The median is the middle value in an ordered dataset, splitting the data into two equal halves.

• When data points are arranged from smallest to largest, the median is the central value if the number of observations is odd.
• For an even number of observations, the median is the average of the two middle values.
• The median is robust against outliers and skewed data, making it useful in electrical measurements affected by occasional spikes or faults.
• It provides a better measure of central tendency than the mean when data is not symmetrically distributed.
• For example, median power consumption readings can indicate typical usage without distortion from unusually high or low values.

Worked Example

A technician at Kenya Power measures the following current values (in amperes): 14, 16, 15, 18, 17, 19.

Arrange the values in ascending order: 14, 15, 16, 17, 18, 19

Since there are 6 values (even number), the median is the average of the two middle values:

• Middle values: 16 and 17
• Median:$$\text{Median} = \frac{16 + 17}{2} = 16.5 \text{ amperes}$$

Answer: The median current is 16.5 amperes.

2.1.3 Mode: Identification and Usefulness

The mode is the most frequently occurring value in a dataset, representing the value with the highest frequency.

• It is the only measure of central tendency that can be used with nominal data, such as types of electrical faults or categories of equipment.
• The mode helps identify common values or recurring issues, such as the most frequent voltage level or common fault code.
• Datasets can have no mode, one mode (unimodal), or multiple modes (multimodal).
• In quality control, identifying the mode of defect types can guide maintenance priorities.
• The mode is simple to compute and interpret, especially for categorical data.

Worked Example

A technician at Bamburi Cement records the following number of faults per day: 2, 3, 3, 4, 5, 3, 2, 4.

Identify the mode:

• Frequency of each value:
  • 2 occurs 2 times
  • 3 occurs 3 times
  • 4 occurs 2 times
  • 5 occurs 1 time

The most frequent value is 3.

Answer: The mode is 3 faults.

2.1.4 Choosing the Appropriate Measure

Selecting between mean, median, and mode depends on the nature of the data and the analysis objective.

• Use the mean for symmetric, continuous numerical data without outliers, such as steady voltage readings.
• Use the median when data is skewed or contains outliers, such as current measurements during faults.
• Use the mode for categorical data or to identify the most common value in a dataset.
• Consider the context of the electrical system and data distribution before choosing the measure.
• Often, comparing mean and median together provides insights into data skewness.

Chapter Summary

This chapter covered the fundamental concepts of statistics and probability essential for engineering technicians. It began with measures of central tendency, explaining how to calculate the mean, mode, and median to summarize data sets. The chapter then explored measures of dispersion, highlighting how variance and standard deviation quantify data spread around the mean. Probability was defined as the likelihood of events occurring, followed by the explanation of the basic laws governing probability calculations. Expectation, variance, and standard deviation were revisited in the context of random variables, with detailed methods for handling both discrete and continuous types. The chapter introduced key probability distributions including binomial, Poisson, and normal distributions, describing their characteristics and applications. Finally, it demonstrated how to compute the mean, variance, and standard deviation for these distributions and applied probability distributions to solve practical engineering problems.