Are you confused about the difference between median and average? You’re not alone. These two terms are often used interchangeably, but they actually have distinct meanings. In this article, we’ll explore the differences between median and average and when to use each one.
Let’s define our terms. The median is the middle value in a set of numbers. If you were to line up all the numbers in a set from smallest to largest, the median would be the one in the middle. If there are two middle numbers, you take the average of those two. The average, on the other hand, is the sum of all the numbers in a set divided by the total number of numbers.
Now that we know what median and average mean, let’s explore when to use each one. In general, the median is a better measure of central tendency when there are outliers or extreme values in the data set. This is because the median is not affected by outliers in the same way that the average is. On the other hand, the average is a better measure of central tendency when the data set is normally distributed, meaning that the majority of the values fall close to the mean.
Define Median
Median is a statistical measure that represents the middle value of a data set. It is the value that separates the lower half of the data from the upper half. To calculate the median, the data must first be arranged in order from lowest to highest or highest to lowest. If there is an odd number of data points, the median is the middle value. If there is an even number of data points, the median is the average of the two middle values.
Define Average
Average, also known as mean, is a statistical measure that represents the central value of a data set. It is calculated by adding up all the values in the data set and dividing by the number of data points. The average is affected by extreme values, also known as outliers, which can skew the result. There are different types of averages, such as arithmetic mean, geometric mean, and harmonic mean, each used for different purposes.
How To Properly Use The Words In A Sentence
When it comes to discussing data, the terms median and average are often used interchangeably. However, they have distinct meanings and uses. It’s important to understand the difference between these two terms to use them correctly in a sentence.
How To Use Median In A Sentence
The median is the middle value in a dataset when the values are arranged in order. To use median in a sentence, consider the following example:
- The median income for households in this area is $60,000.
In this sentence, the word median is used to describe the middle value of household incomes in the area. It’s important to note that the median is not affected by extreme values, or outliers, in the dataset. For example, if one household had an income of $1 million, it would not significantly affect the median income for the area.
How To Use Average In A Sentence
The average, also known as the mean, is the sum of all values in a dataset divided by the number of values. To use average in a sentence, consider the following example:
- The average score on the test was 85%.
In this sentence, the word average is used to describe the typical score on the test. It’s important to note that the average can be affected by extreme values, or outliers, in the dataset. For example, if one student scored a perfect 100%, it would increase the average score for the test.
When using median and average in a sentence, it’s important to consider the context and purpose of the data being discussed. If the dataset has extreme values, the median may be a better measure of central tendency. If the dataset is relatively normal, the average may be a more appropriate measure.
More Examples Of Median & Average Used In Sentences
In order to further understand the difference between median and average, it can be helpful to see them used in context. Here are some examples of how both terms can be used in a sentence:
Examples Of Using Median In A Sentence
- The median income for households in this area is $75,000.
- After removing the highest and lowest scores, the median test score was 85.
- The median age of the participants in the study was 32 years old.
- Half of the homes in this neighborhood have a median value of over $500,000.
- The median price for a gallon of gas in this state is $2.50.
- The median height for adult females in the United States is 5’4″.
- When looking at the distribution of grades, the median grade was a B.
- The median time it takes to complete this course is 12 weeks.
- The median number of children per household in this town is 2.
- After removing the outliers, the median weight of the samples was 150 pounds.
Examples Of Using Average In A Sentence
- The average temperature in this city during the summer is 85 degrees Fahrenheit.
- The average lifespan for a domestic cat is 15 years.
- The average height for adult males in the United States is 5’9″.
- On average, it takes 30 minutes to drive from this city to the airport.
- The average salary for a software engineer in this area is $90,000.
- The average weight of a newborn baby is around 7 pounds.
- The average price for a cup of coffee at this café is $3.50.
- The average number of hours worked per week for employees in this company is 40.
- The average time it takes to complete this task is 2 hours.
- The average number of customers who visit this store per day is 200.
By seeing these terms used in sentences, it becomes clearer how they differ from one another. While both median and average are measures of central tendency, they each have their own specific uses and applications.
Common Mistakes To Avoid
When it comes to statistics, it’s easy to get confused between median and average. These two terms are often used interchangeably, but they are not the same thing. Here are some common mistakes people make when using median and average interchangeably:
Mistake #1: Assuming That The Median And The Average Are The Same Thing
One of the biggest mistakes people make when it comes to median and average is assuming that they are the same thing. While both of these measures are used to describe the central tendency of a dataset, they are calculated differently.
The median is the middle value in a dataset when the values are arranged in order from lowest to highest. On the other hand, the average (also known as the mean) is calculated by adding up all the values in a dataset and dividing by the number of values.
For example, let’s say you have the following dataset:
| Values |
|---|
| 2 |
| 4 |
| 6 |
| 8 |
| 10 |
The median of this dataset is 6, as it is the middle value. The average, however, is calculated by adding up all the values and dividing by the number of values (which is 5 in this case). So, the average of this dataset is (2+4+6+8+10)/5 = 6.
Mistake #2: Using The Median Or Average Without Considering The Distribution Of The Data
Another common mistake people make when using median and average is using one or the other without considering the distribution of the data. The median is a good measure of central tendency when the data is skewed or has outliers, while the average is a good measure of central tendency when the data is normally distributed.
For example, let’s say you have the following two datasets:
| Dataset 1 | Dataset 2 |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 100 | 4 |
| 200 | 5 |
Dataset 1 is normally distributed, while dataset 2 is skewed. In dataset 1, the median and the average are the same (2), while in dataset 2 the median is 3 and the average is 3.0. This is because dataset 2 has an outlier (100) that is pulling the average up.
Therefore, it’s important to consider the distribution of the data before using the median or average as a measure of central tendency.
Tips On How To Avoid Making These Mistakes
Here are some tips on how to avoid making these mistakes in the future:
- Always calculate both the median and the average when analyzing a dataset.
- Consider the distribution of the data before using the median or average as a measure of central tendency.
- Use the median when the data is skewed or has outliers, and use the average when the data is normally distributed.
- Be sure to label which measure of central tendency you are using in your analysis to avoid confusion.
Context Matters
When it comes to analyzing data, one of the most fundamental decisions you will need to make is whether to use the median or the average. However, the choice between these two measures can depend heavily on the context in which they are used.
Different Contexts
Let’s take a look at some examples of different contexts and how the choice between median and average might change:
Example 1: Income
Suppose you are analyzing the income of a group of individuals. In this case, the choice between median and average will depend on the distribution of income. If the distribution is heavily skewed, with a few individuals earning extremely high incomes, then the median may be a better measure of central tendency. This is because the median is not influenced by extreme values in the same way that the average is. On the other hand, if the distribution is relatively symmetrical, then the average may be a more appropriate measure.
Example 2: Test Scores
Now let’s consider a different context, such as analyzing test scores. In this case, the choice between median and average may depend on the purpose of the analysis. If the goal is to understand the typical performance of students, then the median may be more appropriate. This is because the median represents the score that separates the top 50% from the bottom 50%. On the other hand, if the goal is to understand the overall performance of the group, then the average may be more useful.
Example 3: Housing Prices
Finally, let’s consider the context of analyzing housing prices. In this case, the choice between median and average may depend on the type of housing being analyzed. For example, if you are analyzing the prices of luxury homes, then the average may be more useful as it takes into account the high prices of these properties. On the other hand, if you are analyzing the prices of affordable housing, then the median may be more appropriate as it represents the price that separates the top 50% from the bottom 50%.
As you can see, the choice between median and average can depend heavily on the context in which they are used. It is important to carefully consider the purpose of your analysis and the nature of the data before making a decision about which measure to use.
Exceptions To The Rules
While median and average are useful tools for analyzing data, there are some exceptions where the rules for using them might not apply. Here are some explanations and examples for each case:
Outliers
In some cases, outliers can significantly affect the median and average. An outlier is a data point that is significantly different from other data points in the same dataset. When outliers are present, the median may be a better measure of central tendency than the average.
For example, let’s say we are calculating the average income of a group of people. If one person in the group is a billionaire, their income will skew the average significantly higher than the rest of the group. In this case, the median income would be a better representation of the typical income in the group.
Skewed Distributions
When the distribution of data is skewed, the median may be a better measure of central tendency than the average. A skewed distribution is one in which the data is not evenly distributed around the mean.
For example, let’s say we are analyzing the salaries of employees in a company. The majority of employees earn between $40,000 and $60,000 per year, but there are a few executives who earn salaries in the millions. In this case, the distribution of salaries is skewed to the right, and the median salary would be a better representation of the typical salary in the company than the average.
Categorical Data
When dealing with categorical data, such as colors or types of cars, neither the median nor the average can be used to describe the data. In this case, other measures of central tendency, such as mode or frequency, should be used instead.
| Color | Number of Cars |
|---|---|
| Red | 10 |
| Blue | 5 |
| Green | 8 |
| Yellow | 3 |
In the table above, we can see that the most common color of car in the dataset is red, with 10 cars. Therefore, the mode would be a better measure of central tendency than the median or average.
Practice Exercises
Now that you have a better understanding of the differences between median and average, it’s time to put your knowledge to the test. Below are some practice exercises to help you improve your understanding and use of these terms in sentences.
Exercise 1: Calculating Median And Average
Calculate the median and average for the following set of numbers:
| Numbers |
|---|
| 10 |
| 15 |
| 20 |
| 25 |
| 30 |
Once you have calculated the median and average, write a sentence explaining the difference between the two.
Exercise 2: Identifying Median And Average
Identify the median and average for the following set of numbers:
| Numbers |
|---|
| 5 |
| 10 |
| 15 |
| 20 |
| 25 |
| 30 |
Write a sentence explaining which measure of central tendency is most appropriate to use for this set of numbers and why.
Exercise 3: Applying Median And Average
Use median and average in a sentence to describe the following scenarios:
- A class of students took a test. The highest score was 100 and the lowest score was 60.
- A group of friends went out to eat. One friend paid for everyone’s meal, which ranged in price from $10 to $30.
- A company wants to know the average salary of its employees. The salaries range from $30,000 to $100,000.
Include an explanation of why you chose to use either median or average in each sentence.
Answer Key
Check your answers below:
Exercise 1
Median: 20
Average: 20
The median and average are the same in this case because the numbers are evenly distributed.
Exercise 2
Median: 17.5
Average: 17.5
Either the median or average could be used for this set of numbers because they are both the same.
Exercise 3
- The median score on the test was 80, while the average score was 80. This means that half of the students scored above 80 and half scored below.
- The average cost of the meal was $20, with the median cost being $20 as well. This means that half of the meals cost more than $20 and half cost less.
- The average salary of the employees is $65,000, while the median salary is $65,000 as well. This means that half of the employees earn more than $65,000 and half earn less.
The median was used in the first and second sentences because there were extreme values that could skew the data if the average was used. The average was used in the third sentence because the data was not skewed and the values were evenly distributed.
Conclusion
After examining the differences between median and average, it is clear that both have their uses in different situations.
The median is a more reliable measure of central tendency when data is skewed or has outliers, while the average is a better representation of the data when it is evenly distributed.
It is important to understand the differences between these two measures and choose the appropriate one for the situation at hand.
Furthermore, this article highlights the importance of proper grammar and language use in conveying clear and concise information.
By continuing to learn about these topics, readers can improve their communication skills and better understand the world around them.
Shawn Manaher is the founder and CEO of The Content Authority. He’s one part content manager, one part writing ninja organizer, and two parts leader of top content creators. You don’t even want to know what he calls pancakes.