Formula to Calculate Median in Statistics

It is a tool to measure the center of a numerical data set. It summarizes large amounts of data into a single value. One can define it as the middle number of a group of numbers sorted in ascending order. In other words, the median is the number that would have the same amount of numbers both above and below it in the specified data group. It is a commonly used measure of data sets in statisticsIn StatisticsStatistics is the science behind identifying, collecting, organizing and summarizing, analyzing, interpreting, and finally, presenting such data, either qualitative or quantitative, which helps make better and effective decisions with relevance.read more and probability theory.

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Where ‘n’ is the number of items in the data set, and ‘th’ signifies the (n)th number.

Median Calculation (Step by Step)

Examples of Median Formula in Statistics

Example #1

List of numbers: 4, 10, 7, 15, 2. Calculate the median.

  • Firstly, sort the numbers in ascending order. The numbers are ascending when arranged from the smallest to the largest order in that group. The method of finding a median of the odd/even numbers in the group is below. If the number of elements in the group is odd – Find the {(n+1)/2}th term. The value corresponding to this term is the median. If the number of elements in the group is even – Find the {(n+1)/2}th term in that group. The midpoint between the numbers on either side of the median position. For instance, if there are eight observations, a median is (8+1)/2nd position, which is one can compute the 4.5th median by adding the 4th and 5th terms in that group, which is then divided by 2.

Solution: Let us arrange the numbers in ascending order.

In ascending order, the numbers are: 2,4,7,10,15

There are a total of 5 numbers. Median is (n+1)/2th value. Thus, the Median is (5+1)/2th value.

Median = 3rd value.

The 3rd value in list 2, 4, 7, 10, 15 is 7.

Thus, the median is 7.

Example #2

Suppose there are 10 employees in an organization, including the CEO. CEO Adam Smith believes that the salary drawn by the employees is high. Therefore, he wants to gauge the salary drawn by the group and hence make decisions.

Mentioned below is the salary given to the employees in the firm. Calculate the median salary. The salaries are $5,000, $6,000, $4,000, $7,000, $8,000, $7,500, $10,000, $12,000, $4,500, $10,00,000

Solution:

Let us first arrange the salaries in ascending order. Salaries in ascending order are:

$4,000, $4,500, $5,000, $6,000, $7,000, $7,500, $8,000, $10,000, $12,000, $10,00,000

Therefore, the calculation of the median will be as follows:

Since there are 10 items, the median is (10+1)/2 th item. Median = 5.5th item.

Thus, the median is the average of the 5th and 6th items. For example, the 5th and 6th items are $7,000 and $ 7,500.

= ($7,000 + $7,500)/2 = $7,250.

Thus, the median salary of 10 employees is $7,250.

Example #3

Jeff Smith, the CEO of a manufacturing organization, needs to replace seven machines with new ones. However, he is worried about the cost incurred and calls the firm’s Finance Manager to help him calculate the median cost of the seven new machines.

The Finance Manager suggested that one could purchase new machines if the median price of the machines is below $85,000. The costs are as follows: $75,000, $82,500, $60,000, $50,000, $1,00,000, $70,000, $90,000. Calculate the median cost of the machines. The costs are as follows: $75,000, $82,500, $60,000, $50,000, $1,00,000, $70,000, $90,000.

Solution: 

Arranging the costs in ascending order: $50,000, $60,000, $70,000, $75,000, $82,500, $90,000, $1,00,000.

Since there are 7 items, the median is (7+1)/2nd item, i.e., 4th item. Therefore, the 4th item is $75,000.

Since the median is below $85,000, one can purchase the new machines.

Relevance and Uses

The main advantage of the median over means is that it is not unduly affected by extreme values, which are very high and very low. Thus, it gives an individual a better idea of representative value. For instance, if the weights of 5 people in kg are 50, 55, 55, 60, and 150. Mean is (50+55+55+60+150)/5 = 74 kg. However, 74 kg is not a true representative value as most weights are in the 50 to 60 range. Let us calculate the median in such a case. It would be (5+1)/2th term = 3rd term. The third term is 55 kg, which is a median. Since most of the data is in the 50 to 60 range, 55 kg is a true representative value of the data.

We have to be careful in interpreting what the median means. For instance, when we say that the median weight is 55 kg, not everyone weighs 55 kg. Some may weigh more, and some may weigh less. However, 55 kg is a good indicator of the weight of 5 people.

In the real world, to understand data sets such as household income or household assets, which vary greatly, the mean may be skewed by a small number of very large values or small values. Thus, the median is used to suggest what should be the typical value.

Median Formula in Statistics (with Excel Template)

Bill is the owner of a shoe store. He wants to know which size of shoe he should order. He asks 9 customers what size their shoes are. The results are 7, 6, 8, 8, 10, 6, 7, 9, and 6. Calculate the median to help Bill in his ordering decision.

Solution: We first have to arrange shoe sizes in ascending order.

These are: 6, 6, 6, 7, 7, 8, 8, 9, 10

Below is given data for calculating the median of a shoe store.

Therefore, the calculation of the median in excelMedian In ExcelMEDIAN function in Excel gives the median of a given set of numbers. MEDIAN Identifies the location of the center of a group of numbers in a statistical distribution.read more will be as follows:

In Excel, one can use an inbuilt formula for the median to calculate the median of a group of numbers. Select a blank cell and type this =MEDIAN(B2: B10) (B2: B10 indicates the range you want to calculate the median from).

The median of the shoe store will be –

This article has been a guide to Median Formula in Statistics. Here, we discuss calculating the Median using its formula and practical examples in Excel and a downloadable Excel template. You may learn more about Excel from the following articles: –

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