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The owner of a restaurant wants to find out more about where his patrons are coming from. One day, he decided to gather data about the distance in miles that people commuted to get to his restaurant. People reported the following distances traveled. So here are all the distances traveled. He wants to create a graph that helps him understand the spread of the distances-- this is a key word-- the spread of distances and the median distance that people traveled or that people travel. What kind of graph should he create? So the answer of what kind of graph he should create, that might be a little bit more straightforward than the actual creation of the graph, which we will also do. But he's trying to visualize the spread of information. And at the same time, he wants the median. So what a graph captures both of that information? Well, a box and whisker plot. So let's actually try to draw a box and whisker plot. And to do that, we need to come up with the median. And we'll also see the median of the two halves of the data as well. And whenever we're trying to take the median of something, it's really helpful to order our data. So let's start off by attempting to order our data. So what is the smallest number here? Well, let's see. There's one 2. So let me mark it off. And then we have another two. So we've got all the 2's. And then we have this 3. Then we have this 3. I think we've got all the 3's. Then we have that 4. Then we have this 4. Do we have any 5's? No. Do we have any 6's? Yep. We have that 6. And that looks like the only 6. Any 7's? Yep. We have this 7 right over here. And I just realized that I missed this 1. So let me put the 1 at the beginning of our set. So I got that 1 right over there. Actually, there was two 1's. I missed both of them. So both of those 1's are right over there. So I have the 1's, 2's, 3's, 4's, no 5's. This is one 6. There was one 7. There's one 8 right over here. And then, let's see, any 9's? No 9's. Any 10s? Yep. There's a 10. Any 11s? We have an 11 right over there. Any 12s? Nope. 13, 14? Then we have a 15. And then we have a 20 and then a 22. So we've ordered all our data. Now it should be relatively straightforward to find the middle of our data, the median. So how many data points do we have? 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17. So the middle number is going to be a number that has 8 numbers larger than it and 8 numbers smaller than it. So let's think about it. 1, 2, 3, 4, 5, 6, 7, 8. So the number 6 here is larger than 8 of the values. And if I did the calculations right, it should be smaller than 8 of the values. 1, 2, 3, 4, 5, 6, 7, 8. So it is, indeed, the median. Now, when we're trying to construct a box and whisker plot, the convention is, OK, we have our median. And it's essentially dividing our data into two sets. Now, let's take the median of each of those sets. And the convention is to take our median out and have the sets that are left over. Sometimes people leave it in. But the standard convention, take this median out. And now, look separately at this set and look separately at this set. So if we look at this first bottom half of our numbers essentially, what's the median of these numbers? Well, we have 1, 2, 3, 4, 5, 6, 7, 8 data points. So we're actually going to have two middle numbers. So the two middle numbers are this 2 and this 3, three numbers less than these two, three numbers greater than it. And so when we're looking for a median, you have two middle numbers. We take the mean of these two numbers. So halfway in between two and three is 2.5. Or you can say 2 plus 3 is 5 divided by 2 is 2.5. So here we have a median of this bottom half of 2.5. And then the middle of the top half, once again, we have 8 data points. So our middle two numbers are going to be this 11 and this 14. And so if we want to take the mean of these two numbers, 11 plus 14 is 25. Halfway in between the two is 12.5. So 12.5 is exactly halfway between 11 and 14. And now, we've figured out all of the information we need to actually plot or actually create or actually draw our box and whisker plot. So let me draw a number line, so my best attempt at a number line. So that's my number line. And let's say that this right over here is a 0. I need to make sure I get all the way up to 22 or beyond 22. So let's say that's 0. Let's say this is 5. This is 10. That could be 15. And that could be 20. This could be 25. We could keep going-- 30, maybe 35. So the first thing we might want to think about-- there's several ways to draw it. We want to think about the box part of the box and whisker essentially represents the middle half of our data. So it's essentially trying to represent this data right over here, so the data between the medians of the two halves. So this is a part that we would attempt to represent with the box. So we would start right over here at this 2.5. This is essentially separating the first quartile from the second quartile, the first quarter of our numbers from the second quarter of our numbers. So let's put it right over here. So this is 2.5. 2.5 is halfway between 0 and 5. So that's 2.5. And then up here, we have 12.5. And 12.5 is right over-- let's see. This is 10. So this right over here would be halfway between, well, halfway between 10 and 15 is 12.5. So let me do this. So this is 12.5 right over here. So that separates the third quartile from the fourth quartile. And then our boxes, everything in between, so this is literally the middle half of our numbers. And we'd want to show where the actual median is. And that was actually one of the things we wanted to be able to think about when the owner of the restaurant wanted to think about how far people are traveling from. So the median is 6. So we can plot it right over here. So this right here is about six. Let me do that same pink color. So this right over here is 6. And then the whiskers of the box and whisker plot essentially show us the range of our data. And I can do this in a different color that I haven't used yet. I'll do this in orange. So essentially, if we want to see, look, the numbers go all the way up to 22. So they go all the way up to-- so let's say that this is 22 right over here. Our numbers go all the way up to 22. And they go as low as 1. So 1 is right about here. Let me label that. So that's 1. And they go as low as 1. So there you have it. We have our box and whisker plot. And you can see if you have a plot like this, just visually, you can immediately see, OK, what is the median? It's the middle of the box, essentially. It shows you the middle half. So it shows you how far they're spread or where the meat of the spread is. And then it shows, well, beyond that, we have the range that goes well beyond that or how far the total spread of our data is. So this gives a pretty good sense of both the median and the spread of our data.

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Box and whisker plot: how to construct (video) | Khan Academy

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The owner of a restaurant wants to find out more about where his patrons are coming from. One day, he decided to gather data about the distance in miles that people commuted to get to his restaurant. People reported the following distances traveled. So here are all the distances traveled.

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TI-84 Instructions:    1-Variable Statistics

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TI-84 Instructions:    1-Variable Statistics

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Monday, February 27

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Group Activity: Your group will be assigned 2 or 3 data sets.

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Group Activity: Your group will be assigned 2 or 3 data sets.

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Create a plot/histogram for the given sets.  Then find the mean, median, mode and range.

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A statistician for a basketball team tracked the number of points that each of the 12 players on the team had in one game. And then made a stem-and-leaf plot to show the data. And sometimes it's called a stem-plot. How many points did the team score? And when you first look at this plot right over here, it seems a little hard to understand. Understand we have 0, 1, 2 under leaf you have all of these digits here. How does this relate to the number of points each student, or each player, actually scored? And the way to interpret a stem-and-leaf plot is the leafs contain-- at least the way that this statistician used it-- the leaf contains the smallest digit, or the ones digit, in the number of points that each player scored. And the stem contains the tens digits. And usually the leaf will contain the rightmost digit, or the ones digit, and then the stem will contain all of the other digits. And what's useful about this is it gives kind of a distribution of where the players were. You see that most of the players scored points that started with a 0. Then a few more scored points that started with a 1. And then only one score scored points to started with a 2, and it was actually 20 points. So I'm going to actually write down all of this data in a way that maybe you're a little bit more used to understanding it. So I'm going to write the 0's in purple. So there's, let's see, 1, 2, 3, 4, 5, 6, 7 players had 0 as the first digit. So 1, 2, 3, 4, 5, 6, 7. I wrote seven 0's. And then this player also had a 0 in his ones digit. This player, I'm going to try to do all the colors, this player also had a 0 in his ones digit. This player right here had a 2 in his ones digit, so he scored a total of 2 points. This player, let me do orange, this player had 4 for his ones digit. This player had 7 for his ones digit. Then this player had 7 for his ones digit. And then, let me see, I'm almost using all the colors, this player had 9 for his ones digit. So the way to read this is, you had one player with 0 points. 0, 2, 4, 7, 9 and 9. But you can see, and it's kind of silly saying the zero was a tens digit, you could have even put a blank there. But the 0 lets us know that they didn't score anything in the tens place. But these are the actual scores for those seven players. Now let's go to the next row in the stem-and-leaf plot. So over here, all of the digits start with, or all of the points start with 1, for each of the players. And there's four of them. So 1, 1, 1, and 1. And then we have this player over here, his ones digit, or her ones digit, is a 1. So this player, this represents 11. 1 in the tens place, 1 in the ones place. This player over here also got 11. 1 in the tens place, 1 in the ones place. This player, let me do orange, this player has 3 in the ones place. So he or she scored 13 points. 1 in the tens place, 3 in the ones place. 13 points. And then I will do this in purple. This player has 8 in their ones place. So he or she scored 18 points. 1 in the tens place, 8 in the ones place. 18 points. And then finally, you have this player that has the tens digit is a 2. And then the ones digit is a 0. I'll circle that in yellow. It is a 0. So he or she scored 20 points. So looking at the stem-and-leaf plot, we were able to extract out all of the number of points that all of the players scored. And once again, what was useful about this, is you see how many players scored between 0 and 9 points, including 9 points. How many scored between 10 and 19 points, and then how many scored 20 points or over. And you see the distribution right over here. But let's actually answer the question that they're asking us to answer. How many points did the team score? So here we just have to add up all of these numbers right over here. So we're going to add up, I'll start with the largest, so 20 plus 18 plus 13 plus 11 plus 11-- 13, 11, 11-- plus 9 plus 7 plus 7 again plus 4 plus 2. Did I do that right? We have two 11's, then a 9, then two 7's, then a 4 then a 2, and then these two characters didn't score anything. So let's add up all of these together. So 0 plus 8 is 8, plus 3 is 11, plus 1 is 12, plus 1 is 13, plus 9 is 22, plus 7 is 27, 34, 38, 40. So that gets us to 40. Let me do that one more time. 8, 11, 11, 12, 13, 22, 29, 29, and then 29, 36, 40, and 42. Looks like I actually might have messed-- let me do that one more time. This is the hardest part, adding these up. So let me try that one last time. I'm just going to state where my sum is. So 0, 8, add 3, 11, 12, 13, 22, 29, 36, 40, 42. So it's a good thing that I double checked that. I made a mistake the first time. 4 plus 2 is 6, 7, 8, 9, 10. So we get to 102 points. The team, in total, scored 102 points.

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Stem-and-leaf plots (video) | Khan Academy

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A stem and leaf is a table used to display data. The 'stem' is on the left displays the first digit or digits. The 'leaf' is on the right and displays the last digit. For example, 543 and 548 can be displayed together on a stem and leaf as 54 | 3,8.

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In this video we're going to talk about another way of visualizing data called the histogram, which is a very fancy word for a not so fancy thing. I think it's probably fair to say that the histogram is the most used way of representing statistical data. Let me just show you how to figure out a histogram for some data, and I think you're going to get the point pretty easily. So I have some data here and I want to represent it with a histogram. What we're going to see is how frequent are each of these numbers. And in order to figure that out, let me just write the numbers down, let me just categorize them in their respective buckets. So I have a 1 here. I have a 4, so I want to leave space for the 2, the 3, and put a 4 there. I have a 2. I have a 1. Let me put that 1 on a stack right above that 1. I have a 0-- let me put the 0 to the left of the 1. I want to put them in order. I have a 2, another 2. Let me stack that above my first 2. I have another 1. Let me stack that above my other two 1's. I have another 0. Let me stack it there. I have another 1. Then I have another 2. Another 1. I have two more 0's. 0, 0. I have two more 2's. I have a 3. I have two more 1's. Another 3. And then I have a 6. So no 5's, and then I have a 6. And that space right there was unnecessary. But right here I've listed-- I've just rewritten those numbers and I've essentially categorized them. Now what I want to do is calculate how many of each of these numbers we have. So let me go down here. So I want to look at the frequency of each of these numbers. So I have one, two, three, four 0's. I have one, two, three, four, five, six, seven 1's. I have one, two, three, four, five 2's. I have one, two 3's. I have one 4, and one 6. So we could write it this way. We could write the number, and then we can have the frequency. So I have the numbers 0, 1, 2, 3, 4-- we could even throw 5 in there, although 5 has a frequency of 0. And we have a 6. So the 0 showed up four times in this data set. 1 showed up seven times in this data set. 2 showed up five times, 3 showed up to two times, 4 showed up one time, 5 didn't show up, and 6 showed up one time. All I did is I counted this data set, and I did this first. But you could say how many times do I see a 0? I see it one, two, three, four times. How many times do I see a 1? One, two, three, four, five, six, seven times. That's what we mean by frequency. Now a histogram is really just a plot, kind of a bar graph, plotting the frequency of each of these numbers. It's going to look a lot like this original thing that I drew. So let me draw some axes here. So the different buckets here are the numbers. And that worked out because we're dealing with very clean integers that tend to repeat. If you're dealing with things that the exact number doesn't repeat, oftentimes people will put the numbers into buckets or ranges. But here they fit into nice little buckets. You have the numbers 0, 1, 2, 3, 4, 5, and 6. This is the actual numbers. And then on the vertical axis we're going to plot the frequency. So one, two, three, four, five, six, seven. So that's 7, 6, 5, 4, 3, 2, 1. So 0 shows up four times. So we'll draw a little bar graph here. 0 shows up four times. Draw it just like that. 0 shows up four times. That is that information right there. 1 shows up seven times. So I'll do a little bar graph. 1 shows up seven times. Just like that. I want to make it a little bit straighter than that-- 1 shows up seven times. 2-- I'll do it in a different color-- 2 shows up five times. Do a bar graph, go all the way up to five. 2 shows up five times. 3 shows up two times. We have one 3, two 3's. 4 shows up one time here. 5 doesn't show up at all. So it doesn't even get any height there. And then finally, 6 shows up one time. So I'll do 6 showing up one time. What I just plotted here, this is a histogram. This right here is a histogram. Very fancy word, but I think you will agree it's a fairly simple idea. Figure out the frequency of each of these numbers and then plot the frequency of each of these numbers and you get yourself a histogram.

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Comparing Histograms, Dot Plots and Box Plots

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Comparing Histograms, Dot Plots and Box Plots

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Comparing dot plots, histograms, and box plots

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

# data[].attributes.attachment_link.description
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.