Question

Why do you think there is a huge difference between the mean and median of the shares? Which of these metrics is more representative of the shares?

Answer 1

Mean and median are often presented both as descriptive statistics, but this is actally not the case. The median is a central value of the data. It is that value for which one expects half of the (possible or observed) values being smaller and the other half being larger.

It is more a coincidence that the mean also is (often, but nor always!) quite in the center of the data, but its derivation is completely different. The mean is the result of a probability model over the "errors". One expects the values scattering around a common center, and this centre is determined as the value for which the observed data has the hhighest likelihood. This likelihood has to be calculated from a probability distribution for the deviations of the observed values from this hypothetical center. Maxwell, Herschell and others derived an approprite probability distribution from the simple assumptions that the expectation about the errors is symmetric (positive and negative errors of the same absolute size are expected with the same probability), and that all errors are congeneric (they share the same probability distribution). The result of this derivation is the normal distribution. Calculating the max. Likelihood using the normal distribution leads to the mean as the "best guess" for this assumed center. This is quite a different interpretation than just being the "center of the data".

Answer 2

Difference between the mean and median of the shares

• Calculating the mean involves adding up all the values and dividing the result by the total number of values. By making a list of every number in the set and placing them in order, the median may be obtained. Next, look for the number that lies in the middle of the distribution.
• A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
• The mean is the mathematical average of the numbers that are supplied. As a result, the term "average" is frequently used to refer to the mean in mathematics. The middle score among a group of numbers is called the median. The median indicates that half of the scores are higher and half are lower.

metrics is more representative of the shares

The mean, median, and mode are equal when there is a symmetrical distribution for continuous data. Because it incorporates all of the data in the computations in this situation, analysts frequently utilize the mean. But when a distribution is skewed, the median is frequently the most accurate indicator of central tendency.

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