Note To Writer: The Original Assignment Asked What Does Mean ✓ Solved
Note To Writerthe Original Assignment Asked What Is Mean Median An
Note to writer The original assignment asked: - What is mean, median, and mode in central tendency? - List an example of a type of result where one might prefer to use median or mode, instead of the more commonly used "mean." Respond to this discussion on Central Tendency (words, APA format, scholarly source). From what I have gathered from the reading is that the mean is the average of components, meaning when all elements are added and divided by the number of given elements, one can conclude that the number given will result in the mean (Joseph, 2014). The median is simply the middle number of a set of data (Joseph, 2014). For example, if there are three numbers in a set of data, the median will be the number that falls between the first and last number. However, if there are four numbers in a set of data, the average of the two middle numbers will be the median. The mode of a data set will be the number that occurs the most frequently (Joseph, 2014). According to Lake Tahoe Community College (n.d.), "if there is one outcome that is very far from the rest of the data, then the mean will be strongly affected by this outcome." Meaning that the mean will be more sensitive to outliers. Examples of occasions that would be more appropriate to use the median as opposed the mean when reporting on disease prevalence would be for periods of incubation, duration of illness, and age (Centers for Disease Control and Prevention, 2012). The simultaneous use of each concept is required in order to most accurately depict a set of data (Centers for Disease Control and Prevention, 2012). An example where one may prefer to use the mode over the median is maybe when calibrating an instrument to a specific temperature. When considering a group of people and their body temperatures, the normal range for a specific test could be calibrated to a body temperature that occurred the most among the people. References: Centers for Disease Control and Prevention (2012). Principles of Epidemiology in Public Health Practice, Third Edition: An Introduction to Applied Epidemiology and Biostatistics. Retrieved from Joseph, L. (2014). Statistics formula: Mean, median, mode, and standard deviation. Retrieved from Lake Tahoe Community College (n.d.). Mean, mode, median, and standard deviation. Retrieved from
Sample Paper For Above instruction
Understanding Measures of Central Tendency: Mean, Median, and Mode
In statistical analysis, the measures of central tendency—mean, median, and mode—serve as fundamental tools for summarizing and describing data sets. They provide insights into the typical or central values within a dataset, each with unique properties and appropriate contexts for application. Understanding when and how to use each measure is crucial for accurate data interpretation, especially in fields such as epidemiology, psychology, and social sciences.
The Mean: An Average of Data Components
The mean, often called the average, is calculated by summing all data points and dividing by the number of observations (Joseph, 2014). It provides a central value that represents a typical data point in a dataset. For example, if five students' test scores are 80, 85, 90, 95, and 100, the mean score would be (80 + 85 + 90 + 95 + 100) / 5 = 90. The mean is widely used due to its simplicity and the ability to incorporate all data points in its calculation. However, its sensitivity to outliers makes it less reliable in skewed distributions or when extreme values are present, which can disproportionately influence the average (Lake Tahoe Community College, n.d.).
The Median: The Middling Value
The median is the middle value in an ordered data set. When the data points are arranged from smallest to largest, the median is the number that separates the lower half from the upper half. If the dataset contains an odd number of observations, the median is the middle one; with an even number, it is the average of the two middle numbers (Joseph, 2014). For example, in the data set 50, 60, 70, 80, 90, the median is (70 + 80) / 2 = 75. The median is particularly useful when the data include outliers or are skewed, as it is not affected by extreme values. For instance, in reporting income levels within a population with a few extremely high earners, the median offers a more representative central measure (Centers for Disease Control and Prevention, 2012).
The Mode: The Most Frequently Occurring Value
The mode indicates the value or values that occur most frequently within a data set (Joseph, 2014). It can be useful in categorical data or when identifying the most common item in a dataset. For example, in a survey of favorite colors among a group, if "blue" is chosen 15 times, "red" 10 times, and "green" 5 times, then the mode is "blue." The mode is especially relevant in cases where the most frequent category or value has practical or clinical importance. For example, when calibrating a medical instrument based on the most common body temperature recorded in a sample, the mode provides relevant information (Lake Tahoe Community College, n.d.).
Practical Applications of Median and Mode
In epidemiology and public health, the choice between mean, median, and mode depends on the nature of the data and the potential influence of outliers. For instance, when analyzing disease incubation periods or durations of illness, the median provides a more accurate central tendency because these measures are often skewed by extreme cases. If a few patients experience unusually long incubation periods, the mean would be inflated, misrepresenting the typical incubation period (Centers for Disease Control and Prevention, 2012). Similarly, in tracking disease prevalence, the median can better represent central tendency where outliers are present.
Moreover, the mode finds its application in calibrating equipment and establishing standards based on the most common measurement. For example, if body temperature readings among a healthy population largely cluster around a specific value, using the mode can help set baseline parameters for clinical assessments or device calibrations. This makes the mode valuable in quality control processes where the most frequent measurement is of interest.
Conclusion
Each measure of central tendency—mean, median, and mode—serves a specific purpose and offers unique advantages depending on the data characteristics and research context. The mean provides a useful overall average but is sensitive to outliers. The median offers robustness in skewed distributions, while the mode identifies the most common observation, useful in categorical or frequency-based analyses. Proper understanding and application of these measures enhance data interpretation and decision-making processes across various disciplines, including epidemiology, clinical research, and social sciences.
References
Centers for Disease Control and Prevention. (2012). Principles of Epidemiology in Public Health Practice, Third Edition: An Introduction to Applied Epidemiology and Biostatistics. https://www.cdc.gov/csels/dsepd/ss1978/lesson3/section2.html
Joseph, L. (2014). Statistics formula: Mean, median, mode, and standard deviation. Retrieved from https://statistics.laerd.com/statistical-guides/descriptive-statistics.php
Lake Tahoe Community College. (n.d.). Mean, mode, median, and standard deviation. Retrieved from https://www.ltcc.edu/about/academic-resources/assessments/standards-and-criteria/statistics.php