Sometimes when presented with data, it is possible to identify the middle position of the data by using a single value. This single value is known as the measure of central tendency or measure of central location as is the mode, mean, and median. These values are said the summary statistics.
Describe and contrast mean, median, and mode. What is the difference between mean and median? Which is more sensitive to large outliers? When would you rather use median than mean when reporting on disease prevalence?
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Firstly, the recurrent value in a given set of data is called the mode (Laerd Statistics, 2018). On the other hand, the average value of a dataset is known as the mean whereas the central value of the dataset is called the median (Laerd Statistics, 2018). The mean differs from the median in that it is the average value a given data while the median is the middle-most number in the dataset. Moreover, calculation of mean value is entirely dependent on the total number of values present in a dataset, which is, the summation of members of the dataset divided by the total number values in a dataset (Laerd Statistics, 2018). On the other hand, the numerals present in a dataset affect the median differently. Specifically, if a dataset contains an even number of digits, then the average of the two central-most values gives the median. Then again, if a dataset contains an odd number of digits, then the middle-most value becomes the median (Laerd Statistics, 2018).
Furthermore, outliers affect the mean more as compared to the other measures of central tendency. For instance, if one of the results is way larger than the rest of the data, then the mean is skewed by the outcome. As such, when values are undermined in an observation or close together, the median is the correct measure of central tendency to employ.
How might a study use report findings to its advantage by utilizing mean, median, and mode? Can you list an example of a type of result where one might prefer to use median or mode, instead of the more commonly used "mean" (often interchanged with "average")?
The three measures of central tendency can be utilized interchangeably depending on the situation. For instance, the mean comes in handy in a study aimed at determining a country’s death average. On the other hand, the median should be employed in situations where the outliers in the dataset are significantly extreme as compared to the rest of the data. For instance, in the case of determining the country’s income, it is wise to use the median since their exists areas where income is extremely high which may cause the mean to shoot high whereas the median may remain relatively lower.
Lastly, the mode is utilized to determine the most common value in a given frequency in the circumstances such as the most frequent illness. Notably, the mode does not take numerical values thus its uniqueness from the other measures of central tendency. For example, in a situation where twelve patients have the sicknesses: flu, flu, cold, flu, cold, cold, sore throat, flu, sore throat, cold, flu, sore throat. The mode value of the twelve patients is flu.
Reference
Laerd Statistics. (2018). Mean, Mode and Median - Measures of Central Tendency - When to use with Different Types of Variable and Skewed Distributions | Laerd Statistics. Retrieved from https://statistics.laerd.com/statistical-guides/measures-central-tendency-mean-mode-median.php
