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- Median Formula in Statistics
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**Table of Contents**

## What is the Median Formula in Statistics?

Median is a tool to measure the center of a numerical data set. It summarizes large amounts of data into a single value. Median can be defined as the middle number of a group of numbers that have been sorted in ascending order. In other words, the median is the number which would have the same amount of numbers both above and below it in the specified data group. Median is a commonly used measure of data sets in statistics and probability theory.

Median Formula in Statistics is represented as follows,

**Median Formula ={(n+1)/2}th**

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

### Explanation of the Median Formula in Statistics

The formula for the median can be calculated by using the following two simple steps:

**Step 1:** Firstly, sort the numbers in ascending order. The numbers are said to be in ascending order when it is arranged from the smallest to the largest order in that group.

**Step 2:** Method of finding a median of the odd/even numbers in the group is mentioned 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 and the midpoint between the numbers on either side of the median position. For instance, if there are 8 observations, a median is (8+1)/2th position which is the 4.5
^{th}Median can be computed by adding the 4^{th}and 5^{th}terms in that group which is then divided by 2.

### Examples of Median Formula in Statistics

Let us consider a few examples that would bring clarity to the concept.

#### Median Formula Example #1

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

**Solution:** Let us arrange the numbers in ascending order.

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

Therefore, calculation of the median will be as follows,

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

Median = 3^{rd} value.

The 3^{rd} value in list 2, 4, * 7*, 10, 15 is 7.

**Median will be –**

Thus, the Median is 7.

#### Median Formula Example #2

**Suppose there are 10 employees in an organization including the CEO. CEO Adam Smith is of the opinion that the salary drawn by the employees is high. He wants to gauge the salary drawn by the group and hence make decisions. **

4.9 (927 ratings)

**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, calculation of the median will be as follows,

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

Thus, the median is the average of the 5^{th} and 6^{th} item. 5^{th} and 6^{th} items are $7,000 and $ 7,500.

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

**Median will be –**

Thus, the Median Salary of 10 employees = $7,250.

#### Median Formula – Example #3

**Jeff Smith, the CEO of a manufacturing organization needs to replace 7 machines with new ones. He is worried about the cost to be incurred and hence calls the Finance Manager of the firm to help him calculate the median cost of the 7 new machines. **

**The Finance Manager suggested that new machines could be purchased only 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.

Therefore, calculation of the median will be as follows,

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

**Median will be –**

Since the median is below $85,000, the new machines can be purchased.

### Relevance and Uses of Median Formula

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

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

In the real world, to understand data sets such as household income or household assets, which vary greatly, 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, 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 calculation of median of a shoe store.

Using the above-given information we will do the calculation of median as follows,

Therefore, calculation of the median in excel will be as follows,

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

**Median of shoe store will be –**

Hence, Median = **7**

### Recommended Articles

This has been a guide to Median Formula in Statistics. Here we discuss how to calculate Median using its formula along with practical examples in excel and downloadable excel template. You may learn more about excel from the following articles –

- Examples of Normal Distribution Formula (with Excel Template)
- Standard Normal Distribution Formula
- MEDIAN Formula in Excel
- Excel Lognormal Distribution
- Descriptive Statistics in Excel
- Calculate P-Value in Excel
- Frequency Distribution in Excel
- MODE Function in Excel

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