Measures of central tendency (mean, median, mode) and dispersion (standard deviation) are statistical tools used to summarize data, such as the duration of surgical procedures, which can help infection preventionists identify trends or risks for surgical site infections. The Certification Board of Infection Control and Epidemiology (CBIC) supports the use of data analysis in the "Surveillance and Epidemiologic Investigation" domain, aligning with epidemiological principles outlined by the Centers for Disease Control and Prevention (CDC). The question provides a data set of 2, 2, 3, 4, and 9, and requires determining the correct statement by calculating these measures.
Mean: The mean is the average of the data set, calculated by summing all values and dividing by the number of observations. For the data set 2, 2, 3, 4, and 9:(2 + 2 + 3 + 4 + 9) ÷ 5 = 20 ÷ 5 = 4. Thus, the mean is 4, making Option C correct.
Median: The median is the middle value when the data set is ordered. With five values (2, 2, 3, 4, 9), the middle value is the third number, which is 3. Option A states the median is 2, which is incorrect.
Mode: The mode is the most frequently occurring value. In this data set, 2 appears twice, while 3, 4, and 9 appear once each, making 2 the mode. Option B states the mode is 3, which is incorrect.
Standard Deviation: The standard deviation measures the spread of data around the mean. For a small data set like this, the calculation involves finding the variance (average of squared differences from the mean) and taking the square root. The mean is 4, so the deviations are: (2-4)² = 4, (2-4)² = 4, (3-4)² = 1, (4-4)² = 0, (9-4)² = 25. The sum of squared deviations is 4 + 4 + 1 + 0 + 25 = 34. The variance is 34 ÷ 5 = 6.8, and the standard deviation is √6.8 ≈ 2.61 (not 7). Option D states the standard deviation is 7, which is incorrect without further context (e.g., a population standard deviation with n-1 denominator would be √34 ≈ 5.83, still not 7).
The CBIC Practice Analysis (2022) and CDC guidelines encourage accurate statistical analysis to inform infection control decisions, such as assessing surgical duration as a risk factor for infections. Based on the calculations, the mean of 4 is the only correct statement among the options, confirming Option C as the answer. Note that the standard deviation of 7 might reflect a miscalculation or misinterpretation (e.g., using a different formula or data set), but with the given data, it does not hold.
[References:, CBIC Practice Analysis, 2022., CDC Principles of Epidemiology in Public Health Practice, 3rd Edition, 2012., , ]
