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Statistics is an area of applied mathematics that deals with central tendency metrics, including mean, median, and mode. The median is the middlemost value in a data set, while the mean is the average of a specified number of elements in a data set. The total collection of values in a data set is represented by the center value. It’s calculated by dividing the total number of data values by the total number of observations in the data collection.
Definition of Mean
The mean of a data set is the ratio of the sum of all values to the total number of items in the data set. A data set’s mean (average) is calculated by adding all of the numbers together and dividing the total by the number of values in the set.
The arithmetic mean is the most common and often used sort of mean.
Mean Formula = (Sum of all the observations/number of observations).
Definition of Median
The median is the value in a data collection in the middle. The data set is organized in ascending order before the median is calculated. The median is now defined as the value in the middle. If the total number of items in the list is odd, the middlemost value is the median after the elements are arranged in ascending order.
Median Formula
When the number of items in a data set is even –
[(n/2)th term + ((n/2) + 1)th term] / 2.
Here, n is the total number of observations.
When the number of items in a data set is odd-
[(n+1)/2]th
Here, n is the total number of observations.
Example: Let’s solve one question to find out how to calculate mean and median:
Mean
Assume a class of nine students has the following test scores: 2, 4, 5, 7, 8, 10, 12, 13, 83. The average (or mean) here is the sum of all the numbers divided by the total number of observations given, i.e. 144/9.
Median
Assume a class of nine students has the following test scores: 2, 4, 5, 7, 8, 10, 12, 13, 83.
On the other hand, the median is the point at which half the scores are higher and half are lower. As a result, the median, in this case, is 8 because 8 is in the middle of the series given. As a result, the number 8 denotes the central tendency, i.e. median.
Difference between Mean and Median-
>It’s quite easy to use
</th| Mean | Median |
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The mean is found by dividing the number of observations by the sum of all the values in the data array |
The data set’s median is the exact mid-value. It is calculated by arranging the data set in ascending order and then determining or selecting the data set’s central value |
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It is more extensively used in the industry due to the ease with which the average can be computed, and it provides us with a quick number |
Although it is more precise than the mean, it is not widely used in the industry, which is just a simple sum of data |
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It is commonly used for data sets that are skewed |
It is easy to explain the dataset when the data has a significant skewness or a lengthy tail, it’s commonly employed when outliers have a lot of weight in the data, and the mean isn’t a good way to calculate it |
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It is not a reliable method for calculating the central tendency |
It’s a reliable tool since it determines the data’s weight, often higher at the longer tails |
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It is complex |
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It can’t be calculated for categorical data because the values can’t be added together |
It cannot identify categorized nominal data since it is unable to organize it rationally |
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Formula- The sum of all observations to the total number of observations is used to determine the arithmetic mean for ‘n’ observations |
The formula for calculating the median is as follows: [(n+1)/2]th term for an odd number of observations.[(n/2)th term + ((n/2) + 1)th term] / 2 for an even number of observations, where ‘n’ is the total number of observations |
Conclusion
After going over the facts above, we may conclude that these two mathematical notions are distinct. The arithmetic mean, often known as the mean, is the best measure of central tendency since it has all of the characteristics of an ideal measure. Still, it has one flaw: sample fluctuations influence the mean.
Similarly, the median has a clear definition and is simple to grasp and compute.
