Mean Median Mode Problem Solving

The statistical concept of the median is a value that divides a data sample, population, or probability distribution into two halves.

Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers.

While this can be confusing, simply remember that even though the median sometimes involves the computation of a mean, when this case arises, it will involve only the two middle values, while a mean involves all the values in the data sample.

In the odd cases where there are only two data samples or there is an even number of samples where all the values are the same, the mean and median will be the same.

Similarly, or rather confusingly, the sample mean in statistics is often indicated with a capital X̄.

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Given the data set 10, 2, 38, 23, 38, 23, 21, applying the summation above yields: As previously mentioned, this is one of the simplest definitions of the mean, and some others include the weighted arithmetic mean (which only differs in that certain values in the data set contribute more value than others), and geometric mean.We can eliminate answer choices and , because of the above statement. Case 1: Mode: Median: Mean: Since the mean does not equal the median or mode, can also be eliminated.Case 2: Mode: Median: Mean: We are done with this problem, because we have found when , the condition is satisfied. Similarly to mean and median, the mode is used as a way to express information about random variables and populations.Unlike mean and median however, the mode is a concept that can be applied to non-numerical values such as the brand of tortilla chips most commonly purchased from a grocery store.Note that when calculating the median of a finite list of numbers, the order of the data samples is important.Conventionally, the values are listed in ascending order, but there is no real reason that listing the values in descending order would provide different results.Proper understanding of given situations and contexts can often provide a person with the tools necessary to determine what statistically relevant method to use.In general, mean, median, mode and range should ideally all be computed and analyzed for a given sample or data set since they elucidate different aspects of the given data, and if considered alone, can lead to misrepresentations of the data, as will be demonstrated in the following sections.This value is clearly not a good representation of the seven other values in the data set that are far smaller and closer in value than the average and the outlier.This is the main advantage of using the median in describing statistical data when compared to the mean.

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