5.1 Measures of Central Tendency

Measures of central tendency represent the center point or typical value in a dataset. For human resource data in Kenya, these measures help summarize employee performance ratings, salary scales, or recruitment test scores, providing a snapshot that supports decision-making. The three main measures are the mean, mode, and median, each applicable depending on the data type and distribution.

5.1.1 Mean

The mean or arithmetic average is the sum of all data points divided by the number of points. It is widely used in HR to calculate average salaries, average training hours, or average employee appraisal scores, offering a balanced view of overall performance or compensation.

$$\text{Mean} = \frac{\sum x_i}{n}$$

where \(x_i\) represents each data value and \(n\) the total number of values.

Worked Examples

Example 1: Calculate the mean monthly salary of five employees in a retail business: Ksh 30,000; Ksh 35,000; Ksh 28,000; Ksh 40,000; Ksh 32,000.

Given: Salaries = 30,000; 35,000; 28,000; 40,000; 32,000 Ksh, \(n=5\)

$$\text{Mean} = \frac{30,000 + 35,000 + 28,000 + 40,000 + 32,000}{5}$$

$$= \frac{165,000}{5}$$

$$= 33,000 \text{ Ksh}$$

Answer: 33,000 Ksh

Example 2: An HR manager records training hours for 7 employees as: 12, 15, 10, 18, 14, 16, 13 hours. Find the average training hours.

Given: Training hours = 12, 15, 10, 18, 14, 16, 13, \(n=7\)

$$\text{Mean} = \frac{12 + 15 + 10 + 18 + 14 + 16 + 13}{7}$$

$$= \frac{98}{7}$$

$$= 14 \text{ hours}$$

Answer: 14 hours

Example 3: The performance scores of 8 employees in a SACCO loan appraisal are: 75, 80, 85, 70, 90, 95, 88, 78. Calculate the mean score.

Given: Scores = 75, 80, 85, 70, 90, 95, 88, 78, \(n=8\)

$$\text{Mean} = \frac{75 + 80 + 85 + 70 + 90 + 95 + 88 + 78}{8}$$

$$= \frac{661}{8}$$

$$= 82.625$$

Answer: 82.63 (rounded to two decimals)

5.1.2 Mode

The mode is the most frequently occurring value in a dataset. It is useful in HR to identify the most common salary bracket, the most frequent employee qualification, or the most common response in employee surveys.

Worked Examples

Example 1: In a hotel, the number of years employees have worked are: 3, 4, 3, 5, 6, 3, 5. Find the mode.

Given: Years worked = 3, 4, 3, 5, 6, 3, 5

The value 3 appears 3 times, 5 appears 2 times, others less.

Answer: Mode = 3 years

Example 2: An HR survey records preferred shift times for 10 employees: Morning, Evening, Morning, Night, Morning, Evening, Night, Evening, Evening, Morning. Identify the mode.

Given: Preferences = Morning(4), Evening(4), Night(2)

Both Morning and Evening appear 4 times.

Answer: Modes = Morning and Evening (bimodal)

Example 3: The number of training sessions attended by employees in a cooperative are: 2, 3, 3, 4, 5, 3, 2, 5, 5, 5. Find the mode.

Given: Training sessions = 2(2), 3(3), 4(1), 5(4)

5 appears 4 times, highest frequency.

Answer: Mode = 5 sessions

5.1.3 Median

The median is the middle value when data is arranged in ascending or descending order. It is robust against outliers and useful for salary distributions where extreme values may distort the mean.

Worked Examples

Example 1: Find the median salary of employees earning: Ksh 20,000; 25,000; 30,000; 35,000; 50,000.

Given: Salaries sorted: 20,000; 25,000; 30,000; 35,000; 50,000, \(n=5\) (odd)

Median is the middle value at position \(\frac{n+1}{2} = 3\).

Answer: Median = 30,000 Ksh

Example 2: Find the median training hours for employees with: 8, 10, 12, 14, 16, 18 hours.

Given: Training hours sorted: 8, 10, 12, 14, 16, 18, \(n=6\) (even)

Median is average of values at positions \(n/2=3\) and \(n/2+1=4\):

$$\text{Median} = \frac{12 + 14}{2} = 13 \text{ hours}$$

Answer: Median = 13 hours

Example 3: Monthly performance ratings of 7 employees are: 55, 60, 58, 70, 65, 62, 68. Find the median.

Given: Sorted ratings: 55, 58, 60, 62, 65, 68, 70, \(n=7\)

Median is value at position \(\frac{7+1}{2} = 4\)

Answer: Median = 62

Chapter Summary

This chapter focused on descriptive statistics, starting with measures of central tendency which include the mean, mode, and median, essential for summarizing data by identifying central values. The mean provides the average, the mode identifies the most frequently occurring value, and the median represents the middle value in an ordered data set. Next, the chapter explored measures of dispersion, specifically variance and standard deviation, which quantify the spread or variability of data around the mean, helping to understand data consistency. The concept of skewness was then introduced to describe the asymmetry of data distribution, indicating whether data tails are longer on the right or left. Finally, the chapter covered kurtosis, which measures the peakedness or flatness of the data distribution compared to a normal distribution. Together, these descriptive statistics offer comprehensive tools for analyzing and interpreting data sets in business and other practical contexts.