By the end of this chapter, you will be able to:
Mastering these skills will help you confidently interpret data, making you a valuable problem-solver in any business environment.
Compiled by: John Gitau
Measures of central tendency describe the center point or typical value of a dataset. In HR, these measures help summarize employee-related data such as salaries, years of experience, or training hours. Each measure, mean, mode, and median, captures central tendency differently, making it crucial to select the appropriate one depending on data characteristics.
The mean or average is the sum of all data values divided by the number of values. It is widely used in HR to calculate average salaries, average employee age, or average training hours, providing a clear quantitative summary.
The formula for mean is:
$$ \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} $$
where \( \bar{x} \) is the mean, \( x_i \) are the individual data points, and \( n \) is the number of data points.
Example 1: Calculate the mean monthly salary of 5 employees in a retail company with salaries Ksh 30,000, 25,000, 28,000, 32,000, and 35,000.
Given: Salaries = 30,000; 25,000; 28,000; 32,000; 35,000 Ksh$$ \bar{x} = \frac{30,000 + 25,000 + 28,000 + 32,000 + 35,000}{5} $$$$ \bar{x} = \frac{150,000}{5} $$$$ \bar{x} = 30,000 \text{ Ksh} $$ Answer: The mean monthly salary is 30,000 Ksh
Example 2: An HR manager records the number of training hours for 6 employees as 12, 15, 10, 18, 20, and 15 hours. Find the average training hours.
Given: Training hours = 12, 15, 10, 18, 20, 15$$ \bar{x} = \frac{12 + 15 + 10 + 18 + 20 + 15}{6} $$$$ \bar{x} = \frac{90}{6} $$$$ \bar{x} = 15 \text{ hours} $$ Answer: The mean training hours are 15 hours
Example 3: A cooperative records the years of service of 7 staff members: 5, 8, 12, 7, 9, 10, and 6 years. Calculate the mean years of service.
Given: Years of service = 5, 8, 12, 7, 9, 10, 6$$ \bar{x} = \frac{5 + 8 + 12 + 7 + 9 + 10 + 6}{7} $$$$ \bar{x} = \frac{57}{7} $$$$ \bar{x} \approx 8.14 \text{ years} $$ Answer: The mean years of service is approximately 8.14 years
Example 4: In a county government office, the monthly leave days taken by 8 employees are 2, 3, 4, 1, 5, 2, 3, and 4 days. Find the average leave days taken.
Given: Leave days = 2, 3, 4, 1, 5, 2, 3, 4$$ \bar{x} = \frac{2 + 3 + 4 + 1 + 5 + 2 + 3 + 4}{8} $$$$ \bar{x} = \frac{24}{8} $$$$ \bar{x} = 3 \text{ days} $$ Answer: The mean leave days taken are 3 days
Example 5: A bank records the number of new clients each HR officer recruited monthly: 15, 20, 18, 22, 17, 19, 21. Calculate the mean recruitment per officer.
Given: Recruits = 15, 20, 18, 22, 17, 19, 21$$ \bar{x} = \frac{15 + 20 + 18 + 22 + 17 + 19 + 21}{7} $$$$ \bar{x} = \frac{132}{7} $$$$ \bar{x} \approx 18.86 $$ Answer: The mean recruitment per officer is approximately 18.86 clients
The mode is the value that appears most frequently in a dataset. In HR, mode helps identify the most common employee age, preferred leave duration, or the most frequent salary bracket. It is especially useful for categorical or discrete data.
Example 1: Find the mode of employee age in a school where the ages recorded are 25, 30, 25, 28, 30, 25, 27 years.
Given: Ages = 25, 30, 25, 28, 30, 25, 27
Answer: The mode is 25 years (most frequent age)
Example 2: An HR department records the number of dependents for 10 employees as 2, 3, 2, 4, 2, 3, 1, 3, 3, 2. Determine the mode.
Given: Dependents = 2, 3, 2, 4, 2, 3, 1, 3, 3, 2
Answer: The data is bimodal with modes 2 and 3 dependents
Example 3: In a SACCO, the preferred loan repayment periods (in months) recorded are 12, 24, 12, 36, 24, 12, 24, 24. Find the mode.
Given: Repayment periods = 12, 24, 12, 36, 24, 12, 24, 24
Answer: The mode is 24 months
Example 4: The number of training sessions attended by employees in a hotel over a quarter are: 3, 4, 4, 3, 3, 5, 4, 4. Identify the mode.
Given: Sessions = 3, 4, 4, 3, 3, 5, 4, 4
Answer: The mode is 4 sessions
Example 5: The count of sick days taken by employees in a month at a retail business: 1, 2, 2, 3, 2, 1, 4, 2, 3. What is the mode?
Given: Sick days = 1, 2, 2, 3, 2, 1, 4, 2, 3
Answer: The mode is 2 sick days
The median is the middle value in an ordered dataset. It is useful in HR for representing typical salaries or experience levels when data is skewed, as it is not affected by extreme values.
To find the median:
Example 1: Find the median salary of 7 employees with salaries (Ksh): 20,000; 25,000; 22,000; 30,000; 28,000; 24,000; 26,000.
Given: Salaries unordered = 20,000; 25,000; 22,000; 30,000; 28,000; 24,000; 26,000
Ordered: 20,000; 22,000; 24,000; 25,000; 26,000; 28,000; 30,000
Number of data points \( n=7 \) (odd)
Position of median = \( \frac{7+1}{2} = 4 \)
Answer: Median salary is 25,000 Ksh (4th value)
Example 2: The years of experience of 6 HR officers are 5, 7, 3, 10, 8, 6. Calculate the median years of experience.
Given: Experience = 5, 7, 3, 10, 8, 6
Ordered: 3, 5, 6, 7, 8, 10
Number of data points \( n=6 \) (even)
Positions for median = 3rd and 4th values = 6 and 7$$
\text{Median} = \frac{6 + 7}{2} = \frac{13}{2} = 6.5 \text{ years}
$$
Answer: Median experience is 6.5 years
Example 3: In a university HR department, the number of leave days taken by 9 staff members are: 2, 5, 3, 4, 6, 3, 2, 5, 7. Find the median leave days.
Given: Leave days unordered = 2, 5, 3, 4, 6, 3, 2, 5, 7
Ordered: 2, 2, 3, 3, 4, 5, 5, 6, 7
Number of data points \( n=9 \) (odd)
Position of median = \( \frac{9+1}{2} = 5 \)
Answer: Median leave days is 4 days (5th value)
Example 4: The number of training sessions attended by 8 employees in a bank are: 1, 3, 2, 4, 3, 2, 5, 4. Calculate the median sessions attended.
Given: Sessions = 1, 3, 2, 4, 3, 2, 5, 4
Ordered: 1, 2, 2, 3, 3, 4, 4, 5
Number of data points \( n=8 \) (even)
Positions for median = 4th and 5th values = 3 and 3$$
\text{Median} = \frac{3 + 3}{2} = 3
$$
Answer: Median training sessions attended is 3
Example 5: A SACCO records monthly loan amounts (in Ksh) of 10 members: 50,000; 60,000; 55,000; 70,000; 65,000; 60,000; 75,000; 55,000; 50,000; 65,000. Find the median loan amount.
Given: Loans = 50,000; 60,000; 55,000; 70,000; 65,000; 60,000; 75,000; 55,000; 50,000; 65,000
Ordered: 50,000; 50,000; 55,000; 55,000; 60,000; 60,000; 65,000; 65,000; 70,000; 75,000
Number of data points \( n=10 \) (even)
Positions for median = 5th and 6th values = 60,000 and 60,000$$
\text{Median} = \frac{60,000 + 60,000}{2} = 60,000
$$
Answer: Median loan amount is 60,000 Ksh
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Create a free accountThis chapter covered the fundamental concepts of descriptive statistics essential for business mathematics. It began with measures of central tendency, explaining how the mean, mode, and median provide different ways to identify the central point of a data set. The discussion then moved to measures of dispersion, focusing on variance and standard deviation, which describe the spread or variability of data around the mean. Next, the chapter introduced measures of skewness, which assess the asymmetry of data distribution, indicating whether data are skewed to the left or right. Finally, measures of kurtosis were examined to understand the peakedness or flatness of the data distribution compared to a normal curve. Together, these statistical tools enable effective summarization and interpretation of data in a business context. Mastery of these concepts supports informed decision-making based on data analysis.
The monthly salaries (in Ksh thousands) of 5 HR officers are: 40, 45, 50, 55, and 60. Calculate the mean salary. (2 marks)
In a sample of employee ages: 22, 25, 25, 28, 30, 30, 30, 32, 35, find the mode of the ages. (2 marks)
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