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Bar Graph Definition and Examples

Bar graph definition: A visual way to EASILY compare quantities. Bar graphs are graphs (just like any other graph) and the point of them is to compare data.

Bar graphs have three keys items that make them special.

1. Easy To Read: You only have to look at a few things to understand what each bar graph is comparing. They’re big. They’re colorful. You can easily see trends like increasing, decreasing, or flat.

2. Customizable: On any bar graph, you can change several parts of it to make it work better for you. You can change the scale to measure very small (or very large) quantities. You can double or triple them by putting bars beside each other. Bar graph configurations are endless.

3. Easy to Make: Bar graphs aren’t complicated. They just compare numbers. They compare groups. Once you understand their parts, you’ll see they’re easy to make.

If you worked at a sandwich shop, you could make a bar graph of how many sandwiches you sold this week. You could have bars for each day of the week. You could even have different groups showing the different kinds of sandwiches. Making a bar graph would show you what are the most popular sandwiches, and which day of the week you are the busiest.

In the video, you’ll see a bar graph called “Favorite Movie Type by Grade Level.” It shows four groups of movies: Action, Documentary, Drama, and Sports. If you look closely, you’ll see that this is a special bar graph called a double bar graph. We don’t just show one grouping of people, we show two. The blue bars show the favorite movie type for kids in Grade 10, the red bars show the favorite movie type for kids in Grade 11. Each category has both groups.

Also in the video, you’ll see how easy bar graphs are to make.

First you draw the axes. We draw the vertical axis, which uses numbers to compare. Then going left and right we draw the horizontal axis, which uses categories to group things.

The vertical axis on this graph is measuring Hot Air Balloons. They are measured individually.

The horizontal axis on this graph is measuring months of the year. For this example, we use June, July, and August.

Then all we have to do is count and show the number of hot air balloons that get flown in each month.

Each bar graph needs a title. This title shows what we’re measuring, hot air balloons made (by month).

Finally, the graph needs a key. In the example shown, the green bar shows the number of hot air balloons.

Take a look at the video for explanation and examples.

What is a Bar Graph?

Bar graphs are one of the best ways to show a lot of data all in the same image. It is a simple way to show different kinds of data, changes in data over time, or compare lots of things all on the same chart. It is easy to learn, especially when you learn the key parts.

(You can also watch the video at the end of the page!)

Every bar graph has a few common parts:

Bar Graph Title
Horizontal Axis (with units)
Vertical Axis (with units)
Bar Graph Key (sometimes called a Bar Graph Legend)

Let’s break down each part:

Bar Graph Title

Every single graph should have a title. Bar graphs are the same. They are simple to read, but if the graph doesn’t have a title, you’ll be lucky to understand what it’s about. A title should be a summary of the data shown. The title should say what is being measured. Good titles will often have other information. Some times this secondary information will be in parentheses.

For instance, the title of your bar graph could be “Sales”. This shows that the information below will explain the amount of sales. A better title would be “Car Sales”. This shows that you are measuring the sales of a specific product, cars. An even better title would be “Car Sales (Europe & Asia)”. This shows that you are measuring car sales in two specific regions of the world.

Horizontal Axis (with units)

The horizontal axis of a bar graph is the line going from left to right, typically at the bottom of the graph. It should have labels at each step along the graph that define what information is being shown. The horizontal axis of the bar graph can be tricky. Bar graphs can show lots of information, which means that each horizontal axis is different.

Horizontal axes can show movies, cars, colors, anything! The key thing is that you need to show the units. If you don’t write out what each graph is, no one will know. Showing the units is important.

Here are a few examples.

Vertical Axis (with units)

The vertical axis of a bar graph is the line going up and down, typically on the left side of the graph. This axis is counting objects. It will have many measurements marked along it, going from small to large. Each vertical axis will look different. Some will count by ones, some by fives, some by tens, some by hundreds, etc. The key information is that you know where to look to find the total number of objects. As always, the units must be included to give full understanding.

Here are a few examples.

Bar Graph Key (Bar Graph Legend)

Every graph should have a key (sometimes called a legend). The key shows what each bar is displaying. If there are multiple patterns or colors of a graph, they key is where you tell what each color represents.

The key (legend) is shown in the images below.

Bar Graph Review

Bar graphs help count things. They can count small numbers and large numbers. They show comparisons between things. It is a very easy way to show a comparison. When you learn the parts of a bar graph, you’ll learn that they are easy to read and easy to use.

Stem and Leaf Plot with Decimals

It always seems like textbooks like to teach you a topic, give an extremely easy example problem and then give you a twist on your homework problems. Trying to understand a Stem and Leaf Plot with Decimals is one of these tricks. The example is easy, everything is in order and fits nicely, and then there’s a twist.

Luckily decimals really don’t make stem and leaf plots THAT much more difficult. You begin with the same steps as regular problems. If the numbers in the group aren’t already in order, you still have to list them in order, smallest to largest. Then we know the leaves will be the digit on the far right of each number. Here is where decimals get tricky.

Decimal Between Stem and Leaf

If you have a number like 12.3 you would make “12” the stem and “3” the leaf. That’s right, the decimal doesn’t even matter. Since the decimal is in the place of the vertical line separating the stem and leaf, we don’t have to worry about it.

So how do you tell the difference between 12.3 and 123? Good question.

The answer lies with the stem and leaf plot key. Especially in stem and leaf plots with decimals, the key is very important, because it shows where the decimal goes. For the example 12.3, the Key would show that 12 | 3 equals 12.3 units.

Decimal In the Stem

Let’s look at a similar example. If we had the number “1.23” and wanted to put it on a stem and leaf plot, we would have to look at it differently. The leaf should only be one digit, so this makes our stem “1.2”. In this case, the decimal DOES show up, since it has a place within the stem. The leaf would simply be “3”.

You should always include a key, even though no one should get this one confused. For nothing else, the key will show what units you are working in. Even though no one will confuse 1.23 with 123, if you left out the key we wouldn’t know if you were talking about seconds, dollars, inches, etc. For this example we would show the key is – 1.2 | 3 equals 1.23 units.

Mean, Median, Mode, In Reverse

When we are first taught about mean, median, and mode in algebra our first homework problems typically go something like this: Find the mean median and mode of the following set of numbers, 2, 5, 6, 6, 8, 10, 12. Everything is a whole number, they are already in order, and there are minimal calculations needed.

(For those of you keeping score, and since I know you took the time to figure it out 😉 the mean of that set was 7, median = 6, and mode = 6. Good job!)

But then things get a little harder. Fast forward to the last section of your homework and guess what?

EVERYTHING IS REVERSED!

You’re given the mean, median, and mode but not the numbers. You have to create the set of numbers. You were probably never shown how to do this because it’s not as easy as giving someone a formula. Most of the time people can fumble around on a problem like this and accidentally get an answer. The good news is there are many many ways to do this, because as long as your numbers have the specified values you are ok. But that’s not good enough for us. Here’s what to do.

When Things Are Reversed, Median Comes First

The best plan of action is to start with the median. The reason is simple. There can only be one median, and it MUST be in the middle of the data set. Thus we start with the median value and then strategically add an equal amount of numbers greater than and less than it. Each time we add on one side, we must add on the other.

In an ideal situation we would add the median and move to step #2. But if you are told in the homework problem that the total count of numbers in the set has to be EVEN then we must take another step. Since an even number of data points means there are two numbers “in the middle” we know that the median is the average value of them. In this case we still want to begin with the median, but we will choose two numbers that have the median as their average. Although we can do this many ways, we should keep it simple by choosing the closest numbers.

For example, if we are told our data set must have 14 total numbers and a median of 9, we know we must choose two middle numbers. I would suggest we start with 8 and 10. They average out to be 9, so it is still our median. NOTE: we could also simply choose 9 and 9 as our middle numbers, and that would work. Just be careful because if you do it this way you’ve created a median and a mode, since the number is repeated. Either way,

When Things Are Reversed, Mode Comes Second

After we have chosen one number (or two if we are forced) as our median, the next thing we want to address is the mode. A key thing to remember about mode is that it has to occur most often, but there is no rule as to how many times. So our second step is to add the mode number to our data set a few times. I usually suggest 3 times, because when you calculate mean there must be some room to add numbers to reach the exact calculation, so we should give ourselves some room for error in case a number needs to show up twice. Some times we are told that we can only have a few numbers in our set so space is limited. Regardless, it is best to start with median then add mode.

Remember, when you add the mode, you MUST add other numbers on the other side of the median. So if the mode is less than the median and you added it three times, you must add three numbers to your data set that are greater than the median. I usually just try to add three numbers in a row on the other side of the median.

In some rare cases you will be told there is no mode. This is great actually, because you can skip this step altogether and begin building for the mean.

Now Calculate The Mean In Reverse

Now we have to get very creative. There are many ways to do this next step. This is why some problems can be hard and others can be easy. Remember the mean is the sum of all the numbers divided by how many numbers are in the set. At this point you will have several numbers. But chances are they do not yet have the mean that you desire. So the best way is to put variables in the data set and solve with algebra. This will be a trial and error process, and may involve adding many numbers to your set.

First we add two variables (call them A and B, or whatever you wish) that are less than the median. Then add two variables (C and D) that are greater than the mean. We will take all the numbers and add them. Then algebraically isolate the A + B + C + D and it will equal a specific number. Then try to come up with a successful combination of numbers that add to solve the equation AND obey their place in the set.

This can be complicated, so let’s take a look at some examples.

Mean, Median, Mode in Reverse Examples:

Mean = 20, Median = 23, Mode = 17

First start with the Median number and add it to your set. Then we add the mode. In this case we add 20 three individual times. Our list so far is 20, 20, 20, 23. Since we added three numbers less than 23, we must add 3 numbers that are greater than 23. As you can watch in the video above in a perfect world the three numbers we added here would also have solved the Mean. This would have solved the whole problem.

Instead, since it didn’t work I just decided to add the numbers 24, 25, and 26 since they were greater than 23 but were not too big. With median and mode completed, we needed to move on to the last step. We added a number greater than 23 (variable D) and another less than 23 (variable E).

We substitute all this into the mean formula and get 20 (the mean) = (17 + 17 + 17 + E +23 + 24 + 25 + 26 + D) all divided by 9. We did inverse operations to remove the divided by 9. This means we multiplied both sides by 9. Then we added all the numbers, giving us 149. Our simplified step was 180 = 149 + E + D. We did a second inverse operation to get E + D by itself. This means we subtracted 149 from each side. 180 – 149 gives us 31. Our final equation that we needed to solve was 31 = E + D.

Remember, there are many ways to solve this, but we must choose numbers where one is less than 23 and the other is greater than 23. In this case I just chose E = 4. When this is substituted in we have 31 = 4 + D. This simplifies to D = 27. Our final set of numbers is 4, 17, 17, 17, 23, 24, 25, 26, 27. Remember this is not the ONLY possible answer.

Mean = 20, Median = 20, Mode = 20

In example problems it is common to be given parameters where two or more of them equal the same number. In this case if you’re clever, I know what you are thinking. If we used a set of one number, and that number was “20” we would be finished. Mean, median, and mode all equal 20!

This might work, but some homework problems make you have at least 5 numbers in the set, and they can’t all be the same. If that’s the case, let’s look at how to solve this.

We start with the median, which is 20. Then we move to mode, which is also 20. We will add 20 two more times to our set. Keep it balanced by adding a 20 to the left and one to the right. To get the mean, we know our target needs to be 20. Let’s add two variables, one less than 20 and one greater than 20. Since the first step to finding the mean is adding everything we get A + 20 + 20 + 20 + B. This divided by 5 (since we have 20 three times and an A and a B). All this equals 5.

Do inverse operations to eliminate the divided by 5. Do this by multiplying each side by 5. This leaves us with 100 = A + 60 + B. We do another inverse operation by subtracting each side by 60. This leaves us with 40 = A + B.

Now we are able to be creative. We want A + B to equal 40, but must have A less than 20 and B greater than 20. I just chose A = 15 to proceed. We substitute that into our last formula, which gives us 40 = 15 + B. We subtract 15 from each side and are left with 25 = B. We know our final set of numbers is 15, 20, 20, 20, 25.

Two More Examples of Mean Median Mode in Reverse:

Mean = 8, Median = 7, Mode = 12, #’s in set = 5

In this case our data set can only have 5 numbers, so we must choose wisely. We begin with the median as always. We add 7 to our set. Then we move to the mode. Since the mode is 12 and it must show up more than the others, we just add it twice, since we don’t have much room to spare. Since we added two numbers greater than the median, in order to keep it balanced we must add two numbers less than 7. But be careful because adding these final two numbers is all we have left. We need them to not only be less than 7, but we need them to also solve our mean.

Since as of now we don’t know what the numbers are we will call them variables A and B. We must add all the numbers as the first step to find the mean, so we add A + B + 7 + 12 + 12. We divide this by 5, and the whole thing is equal to 8. We do inverse operations on the 5, which means we multiply each side by 5. 8 times 5 gives us 40, and this equals A + B + 7 + 12 + 12. This simplifies to 40 = A + B + 31. We subtract 31 from each side, giving us 9 equals A + B. A and B both need to be less than 7, so I chose B equals 6. When we substitute this back in we have 9 = A + 6. Subtract 6 from both sides and we have 3 = A. Since both A and B are less than 7 we did not change the median, and since they are different we didn’t change the mode.

Our final answer is 3, 6, 7, 12, 12.

Mean = 15, Median = 7, Modes = 20 and 2, #’s in set > 12

Begin with the median of 7. Next we will add the modes. We are lucky that one mode is less than the median and one is greater than the median, so the set stays balanced when we add them. I chose to add the modes three times each. Right now our set is 2, 2, 2, 7, 20, 20, 20. We must add 6 more numbers to achieve our total set size. As we add numbers we must always keep the mean in mind.

Let’s add variables A, B, and C in the set below 7 and D, E, and F above 7. They don’t yet have to be in order (we can do that later) but it is important to remember that 3 will be less than the median and 3 will be greater than the median. We add everything together and divide it by how many numbers we have. This equals the mean of 15.

So our first algebra step is: 15 = (2 + 2 + 2 + A + B + C + 7 + D + E + F + 20 + 20 + 20) divided by 13. We do inverse operations by multiplying each side by 13. 15 times 13 gives us 195. We add the numbers on the other side which gives us 73 + A + B + C + D + E + F. Subtract 73 from each side, which gives us a simplified version of the mean. 122 equals A + B + C + D + E + F. Here is where we get creative. Since there aren’t too many numbers to choose from that are less than 7, I want to go ahead and just try a few numbers for A, B, and C to see if we could make them work.

Remember, this can be a trial and error process, so beware this step might have to be repeated with other guesses. I chose A = 4, B = 5, and C = 6. We need to substitute these in to see what we have left. 122 = 4 + 5 + 6 + D + E + F. This simplifies to 122 = 15 + D + E + F. Subtract 15 from both sides to get 107 = D + E + F. This means our last step is to pick three numbers than are greater than 7 than all add up to 107. I think we can do this. We don’t want to mess up the modes so I chose D = 10 and E = 30. You can choose what you’d like if you’ve made it this far. We are left trying to find F so that it satisfies our equations. We can substitute in to 107 = 10 + 30 + F to solve for F. Add the 10 and 30 to get 40, and subtract it from both sides. 107 – 40 gives us our answer, 67 = F.

Our final answer to this last example problem is 2, 2, 2, 4, 5, 6, 7, 10, 20, 20 , 20, 30, 67.

Whew, good job. It can be tough on problems that have many possible answers because there is an overwhelming feeling of possibly messing it up. I would love to know what you thought of these example problems. Did they help? Leave a comment below or send me and email at contact@learnalgebrafaster.com.

Mean Pros and Cons

When you come across a large data set, whether it’s survey results or just a homework problem, there are several ways you can try and describe the important aspects of the set. Each of these statistical values have pros and cons. This is a 3 part series highlighting the good, the bad, and the ugly of mean, median, and mode.

Here are links to the other two:

Median Pros and Cons

Mode Pros and Cons

Mean Pros and Cons

All statistical calculations on a large set of numbers involves some work. This is where there is some trade off. Typically the ones that are the most meaningful take the most work. This is true, especially for the mean.

Mean Pros

You do NOT have to put the data in order.
Mean is a very descriptive value.
Represents what each value would be if they were all equal.

Mean Cons

It is one large calculation, often giving you a decimal number.
You must count all the numbers in the set.
Can be skewed due to an outlier.

Overall finding the mean involves the most work. The best news is that it is the most descriptive. It is so descriptive that it is referred to by many people using different terms, like average, and arithmetic mean. This is a common descriptive measure that you have probably seen or used before even if you don’t realize it.

Mean finds the average, and this is very helpful. To put this another way, if all data entries were equal, what would they look like? This is the mean value.

Mean is used in many walks of life, and is a very helpful value from many angles. This article just showed you the pros and cons of mean, but for a video AND article tutorial on how to find the mean check out this article.

Median Pros and Cons

Here are links to the other two:

Mean Pros and Cons

Mode Pros and Cons

Median Pros and Cons

The median is another way to find the MIDDLE of a data set. This is different from the mean, due to the fact that one large outlier doesn’t adversely affect the middle. Median and mean accomplish similar goals with similar outcomes.

Median Pros

It finds the middle of the data set.
It is not affected by one outlier number.
Combined with mean it can be a very descriptive tool.

Median Cons

You MUST put the numbers in order from least to greatest.
The way you find median differs depending on how many numbers are in the group.

Median can be tricky. Finding it depends on whether there are an even amount of numbers in the set or an odd amount of numbers in the set. One involves calculation, the other doesn’t. Median is probably the most labor intensive value to find (out of mean, median, and mode) but it is very useful.

It is robust against wildly different numbers present in the set, unlike mean. In fact, a good way to predict where abnormal numbers lie is to compare median with mean to see which is greater and by how much. Overall median is a good value to know from a data set, and although it takes a lot of work, it is very helpful.

To find out how to find median with a step by step example video and article, click here.

Mode Pros and Cons

Here are links to the other two:

Mean Pros and Cons

Median Pros and Cons

Mode Pros and Cons

All statistical calculations on large data sets involve some work. But with any statistical value, one measurement can’t truly identify all the important aspects of a given data set.

Mode Pros

You do NOT have to put the data in order.
No calculations necessary.

Mode Cons

It is possible to have no mode, one mode, or many modes.
Not a great descriptor of a data set, there is no guarantee that Mode will reflect the greater set.

Overall Mode involves the least work, and unfortunately that pretty much leaves it the least useful. It is possible that the mode and either the median or mean are similar, in which case mode is more relevant. But also in that case you have other values that are weighing the data.

Mode just means there is one specific data point that occurs more than the rest. It doesn’t suggest that it happens near a critical point, just that it happens. Sometimes the mode will be important, but just because it shows up often doesn’t MAKE it important.

Regardless, the mode is relatively easy to find. Although there can be none, one, or many, the mode can help you identify an important value of a large data set. Click here to see a step by step video and article on how to find the mode.

How to Find the Mean

How do you find the mean of a set of numbers? It is one of the more labor intensive values you can find about a data set. Order is not important, but there are two key things to be looking for. Let’s take a look at how to find the mean.

How to Find the Mean

Mean is another word for average. To find this you have to find the sum of all the numbers in the set. After that, you count how many numbers are in the set. We take the total sum and divide that total by how many numbers there are in the set. This gives us the mean of the group.

Don’t worry if this comes out to a decimal. If you are doing this on a homework assignment, either round to the first decimal place or double check the directions to see if there is a rule you should follow. Decimal answers are quite common, so don’t immediately assume you are wrong if you get a decimal.

Mean Example Problem

Let’s find the mean of this set of data:

10, 16, 19, 21, 13, 16, 25, 29, 10, 12, 18, 16, 20, 27, 11, 15

The first thing we need to do is add them all. To see this done step by step, check out the video above. The total sum when everything is added together is 278. Then we count and see that there are 16 individual numbers in the group. Our mean calculation is 278 divided by 16, which gives us a (rounded) answer of 17.4.

Another Mean Example Problem

Let’s find the mean of the following set:

57, 43, 65, 55, 39, 50, 65, 64, 52, 61, 49

Once again, our first step is to add the numbers together. This is also shown in the video above. The numbers added gives us total sum of 600. We then count to see how many numbers there are, which is 11. Our final mean calculation is 600 divided by 11, which gives us a mean of 54.5.

The way we find the mean is the same, no matter how big the list is. It would be the same if the numbers had decimals as well. The mean is the average of all the numbers and is one of the most useful values when trying to understand a large set of numbers.

To learn how to find other values of a set of numbers, check out the other articles in this series:

How to Find the Median

How to Find the Mode

How to Find the Range

How to Find the Midrange

How to Find the Median

How do you find the median of a large group of numbers? The first step is you have to list the numbers in order from least to greatest. Then we find the middle value, which is the median. Some times there is a catch. If there is an even amount of numbers in the set, that means two numbers are technically in the middle. So we have to take an average of those values by adding them and dividing them by two.

How to Find the Median

Finding the median can be tricky, because sometimes it’s straightforward and some times there is calculation involved. First we always put the numbers in order from smallest to largest. Then we can find the middle value several ways. The way that’s shown in the video above is to mark off the least and greatest numbers, and keep doing so until you get to the middle. You can also do a calculation.

Median of Even Set

When you have a set with an even amount of numbers, finding the median is harder. The way you find this is you take the total count of numbers in the set and divide by 2. This gives you only one of the two numbers that make up your median. You must also include the following number. Then you have to take the average of those two.

For instance, if you had a set of 8 numbers, and you had them listed in order. There will actually be two numbers in the middle of the list. To find out which numbers are in the middle you divide 8 by 2, which gives you 4. So if you start with the smallest number and count up, the middle numbers will be the fourth AND fifth (because you must also include the next one). So to find the median you would take numbers 4 and 5, add them, and then divide by two to find your median.

Median of Odd Set

Some times you will have an odd count of numbers. In this case you divide the total count of numbers by 2, and then round UP to the nearest number. This is your median number, because it is in the middle of the set.

For instance, if you had a group of 15 numbers in a set, to find the median you would divide 15 by 2. This gives you 7.5. To find the median we round this number up to 8. Make sure that the numbers are in order from smallest to largest. Your 8th number is in the middle, so it is the median.

Median Example Problem

Let’s find the median of this set of data:

10, 16, 19, 21, 13, 16, 25, 29, 10, 12, 18, 16, 20, 27, 11, 15

When we put these numbers in order from smallest to largest it looks like this:

10, 10, 11, 12, 13, 15, 16, 16, 16, 18, 19, 20, 21, 25, 27, 29

We count how many numbers are in the set, which is 16. Since this is an even number, we have to find the two numbers that are in the middle. We divide 16 by two, which gives us 8. We also include the NEXT number, which will be the 9th number. We start with the smallest number and find out what the 8th and 9th number are. Coincidentally they are both 16. This means automatically that our median is 16.

Remember, if those numbers had been different, we would have to add them and divide by two. Always remember this.

Another Median Example Problem

Let’s find the range of the following set:

57, 43, 65, 55, 39, 50, 65, 64, 52, 61, 49

We begin by putting the numbers in order from least to greatest, which is:

39, 43, 49, 50, 52, 55, 57, 61, 64, 65, 65

We count to see how many numbers are in the set and find out there are 11. We divide 11 by 2, which gives us 5.5. We round it up to the nearest number, which gives us 6. We begin counting from the smallest and see that our 6th number is 55. This is the median of the set.

To learn how to find other values of a set of numbers, check out the other articles in this series:

How to Find the Mean

How to Find the Mode

How to Find the Range

How to Find the Midrange

How to Find the Mode

How do you find the mode of a set of numbers? The good news is you don’t have to rearrange the whole set of numbers to find the range. You do however have to check each value to see which one occurs most often in a set. Remember, it is ok to have multiple modes, so if two or more numbers occur the same amount of times in a data set (more than all the others) they are both the modes.

How to Find the Mode

The mode is one of the easiest statistical values to find in a set of numbers. The only goal is to find the number (or numbers) that happen the most often in the group. You don’t have to remember how many times it shows up, just the number itself.

To find it, scan through the list and record duplicates. Once you’re finished, the number that occurs most is the mode. No calculations are needed, ever. This works on a small group of numbers or a large group. It doesn’t matter if they have decimals or anything else. Just find the one that happens the most.

Mode Example Problem

Let’s find the range of this set of data:

10, 16, 19, 21, 13, 16, 25, 29, 10, 12, 18, 16, 20, 27, 11, 15

When you look through this set of numbers, you see there are more than one 10 and more than one 16. We compare the two and see that 16 is the only number that occurs 3 separate times. 16 is the mode.

Another Mode Example Problem

Let’s find the range of the following set:

57, 43, 65, 55, 39, 50, 65, 64, 52, 61, 49

We see that 65 is only number that is repeated, so it is the mode. Even if it only happens twice, it still happens more than any other number, which is all you need. Although it didn’t happen in the above example, if we had two different numbers that happened twice, they would BOTH be the mode.

To learn how to find other values of a set of numbers, check out the other articles in this series:

How to Find the Mean

How to Find the Median

How to Find the Range

How to Find the Midrange