How To Find the Formula of Median and How It Is Used

If you're working in a career that involves statistics, such as data analysis or market research, you may have used a median formula. The median is the middle value in a data set with the same amount of values above and below it. Understanding how to find the median can help you summarize a large amount of data using a single value for other statistical uses. In this article, we explain how to calculate the formula of median, review examples of how to use the median formula, discuss its advantages, and answer some frequently asked questions.

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What is the formula of median?

The formula of median is used to find the middlemost value after arranging the other values in the data set in ascending order. It's one of the most straightforward statistical measures to calculate and can represent many values with only one value. The formula to find the median depends on how many values are in the data set. In an odd number of values, the middlemost value is the median, and the median is the average of the two middle values for an even number of values. You can also refer to it as the Place Average.

Median is one standard measure of central tendency. The other two measures are:

1. Mean: This is the average of the data set. You can calculate the mean by adding all the data set's values together and dividing the sum by the number of values.

2. Mode: This is the value that occurs most frequently in a data set. You can use the term bi-modal distribution when two values occur the same amount of times in a data set.

How to calculate median in statistics

You can calculate the middle value of an arranged data set by using the median formula. To find this measure of central tendency, it's necessary to put the values of the data set in ascending order. The formula to discover the median differs based on the number of values in the data set and whether they're even or odd. The following formulas can help you find the median of a data set:

1. Median formula with odd data set

You can find the median formula of a data set with an odd number of values using the following steps:

1. Arrange the values in ascending order.

2. Count the number of values, n.

3. Determine if the number of values, n, is odd.

4. The value in the middle of the data set with the same number of values above and below it is the median.

You can express the median formula for a data set with an odd amount of values as the following:

Median = [(n + 1) / 2]th term

2. Median formula when a data set is even

You can find the median formula of a data set with an even number of values using the following steps:

1. Arrange the values in ascending order.

2. Count the number of values, n.

3. Determine if the number of values, n, is even.

4. Locate the two numbers in the middle of the data set.

5. Find the average of the two middle numbers by adding them together and dividing the sum by two.

6. The result of this average is the median.

You can use this calculation to express the median formula for a data set with an even amount of values:

Median = {(n/2)th term + [(n/2) + 1]th term} / 2

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3. The median formula of ordinal data

You may typically use the median formula with numerical data, but you can also find the median of ordinal, or categorically ordered data. You can arrange the ordinal data into categories with a rank order. For example, you can set the level of agreement as strongly disagree, disagree, agree, and strongly agree, or you can arrange language ability level as beginner, intermediate, and fluent. The process for determining the median of an ordinal data set is similar to that of an odd-numbered numerical data set. You can find the median of an ordinal data set using the following steps:

1. Arrange the values in ascending order.

2. Count the number of values, n.

3. Find the middle value using the same median formula for an odd-numbered data set or locate the middlemost value.

You can only use this formula for a data set with an odd number of values, and can't calculate the average of the two middlemost values in an ordinal data set with an even number of values. You can decide to convert the ordinal data into a quantitative format so that you may calculate the two middle values to find the median.

4. The median formula of two values

After arranging the values of a data set in ascending order, the median is the number in the middle of the data set. This can often make it different from the mean. For a data set with two values, the median and the mean are the same. To find the median of two values, you can use the same formula for an even number of values in a data set:

Median = {(n/2)th term + [(n/2) + 1]th term} / 2

Example uses of the median formula

You can use these formulas in the following examples to understand how to apply the median formula:

Odd-number data set

For example, here's how you can calculate the median of a data set with the values 10, 4, 15, 7, and 2:

1. Arrange the data set in ascending order: 2, 4, 7, 10, 15.

2. There are five values.

3. Find the middle value. This is the median.

4. The median in this data set is 7.

5. Use the equation: [(5 + 1) / 2]th term = 3rd term.

6. The third term is 7.

Even-number data set

For example, there are ten employees in a company, including the CEO. The CEO believes that the employees' salaries are too high and wants to compare their salary differences to make a decision. The employees' salaries are $6,000, $5,000, $7,000, $3,000, $7,500, $8,000, $14,000, $10,000, $4,500, and $100,000. To calculate the median of these salaries, you can do the following:

1. Arrange the data set in ascending order: $3,000, $4,500, $5,000, $6,000, $7,000, $7,500, $8,000, $10,000, $14,000, $100,000.

2. There are 10 values.

3. Find the two middle values of the data set.

4. The two median values in this data set are the 5th and 6th values, $7,000 and $7,500.

5. Use the equation: {[10 / 2]th term + [(10 / 2) + 1]th term} / 2 = $7,250.

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

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Advantages of calculating the median

The primary advantage of using the median is that very low or high values won't disproportionally affect the calculations. Using the median, you can have a better value representation if the weight of five people in kg is 50, 55, 55, 60, and 150. The mean is 74kg. This is not sufficiently representative of the data set because most of the weights are between 50kg and 60kg. You can find a potentially more useful value using the median formula:

(5 + 1) / 2nd term = 3rd term

The third term of 55kg is the median. Since most of the weights are between 50kg and 60kg, this median is more representative of the data set than the mean. It's essential to interpret the median within the context of the entire data set. If your data set has several exceptionally small or large data points, this can also skew the mean to be less representative of the data, in which case you may use the median formula instead.

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Frequently asked questions about medians

When working with medians, these are some of the most frequently asked questions:

• What is the median in statistics? The middlemost value is the median of the data. You can find the centre position of a data set by using the median formula.

• What is mean vs. median? The mean is the average of the data set and is equal to the sum of the data divided by the number of values in the data set. The median is the middle value of the data set.

• Why do professionals call the median a place average? You can refer to the median as the positional average because it falls in the middle of a data set after arranging it in ascending order. Within an odd number of values in a data set, the median is the middle value, and when the number of values is even, you can find the median by calculating the average of the two middle values.

• What does "n" represent in the median formula? When using the median formula, "n" represents the number of values in the data set.