Mean Median Mode Problem Solving

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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.

If however the store simply used an average and sold 8 bags of each, it could potentially lose 4 sales if a customer desired only XOCHi TL chips and not any other brand.

As is evident from this example, it is important to take all manners of statistical values into account when attempting to draw conclusions about any data sample.

It is possible for a data set to be multimodal, meaning that it has more than one mode.

For example: 2,10,21,23,23,38,38 Both 23 and 38 appear twice each, making them both a mode for the data set above.The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and are all equal. Since there must be a unique mode, and is already repeated twice, cannot be any of the numbers already listed (3, 4, 5, 7).(If it were, the mode would not be unique.) So must be , or a new number.The equation for calculating an arithmetic mean is virtually identical to that for calculating the statistical concepts of population and sample mean, with slight variations in the variables used: The mean is often denoted as x̄, pronounced "x bar," and even in other uses when the variable is not x, the bar notation is a common indicator of some form of mean.In the specific case of the population mean, rather than using the variable x̄, the Greek symbol mu, or μ, is used.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.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.Similarly, or rather confusingly, the sample mean in statistics is often indicated with a capital X̄.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.


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