Algebra

Histograms | Applying mathematical reasoning | Pre-Algebra | Khan Academy

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In this video we will talk about another way to illustrate data called a histogram, which is a modern word for something not so modern. I think it’s probably correct to say that the histogram is the most commonly used way of presenting data. Let me show you how to make a histogram for some data and I think you will grasp the essence very easily. I have some data here and I want to present them with a histogram. We will see how many times each of these numbers occurs. And to clarify this, let me write the numbers below and categorize them into the appropriate categories. I have 1 here. I have 1. I have 4, I want to leave room for 2, 3 and put 4 here. I also have 2. I also have 1. Let me put this 1 on top, just above the other 1. I have 0 – let me put 0 to the left of 1. I want to put them in order. I have 2, another 2. Let me put it above the first 2. I have another 1. Let him place it above the other 2 units. I have another 0. I’ll put it there. I have another 1. Another 1. Then I have another 2. Another 1! I have two more zeros. 0, 0. I have two more couples. Two 2. I have 3. I have two more units. Two units. Another 3. Then I have 6. No 5, then I have 6. The place there was not necessary. But here I just copied those numbers and I actually categorized them. Now I want to see how many of each of these numbers we have. Let me start from the bottom. I want to look at the frequency of each of these numbers. The frequency of each of these numbers. I have 1, 2, 3, 4 zeros. I have 1, 2, 3, 4, 5, 6, 7 units. I have 1, 2, 3, 4, 5 pairs. I have 1, 2 threes. I have one 4 and one 6. So we can write it this way. We can write the number and then the frequency. The frequency. I have the numbers 0, 1, 2, 3, 4, we can put 5 there too, although 5 has a frequency of 0. We have 6. 0 occurs 4 times in this data table. 1 occurs 7 times in this data table. 2 occurs 5 times in this data table, 3 occurs 2 times, 4 occurs 1 time, 5 does not occur, and 6 occurs 1 time. I just counted this dataset. But you may be wondering how many times we see 0. I see her 1, 2, 3, 4 times. How many times do I see 1? 1, 2, 3, 4, 5, 6, 7 times. This is what we mean by “frequency”. The histogram is actually just a chart, a kind of bar chart, showing the frequency of each of these numbers. It will look very similar to this original thing I drew. Let me draw some axes here. Here the different groups are the numbers. And that’s because we’re dealing with very clean integers, which are repeated. If we work with data where the numbers are not repeated, people will often put numbers in groups or spaces. But here they form nice little groups. We have the numbers 0, 1, 2, 3, 4, 5 and 6. These are the numbers for the moment. And then on the vertical axis we will set the frequency. 1, 2, 3, 4, 5, 6, 7. This is 7, 6, 5, 4, 3, 2, 1. 0 is displayed 4 times. We will make a small bar chart here. 0 is displayed 4 times. I’ll just do it. 0 is displayed 4 times. This is the information over there. 1 is displayed 7 times. I will make a small bar chart. 1 is displayed 7 times. Exactly. I want to make it a little clearer than that – 1 is displayed 7 times. 7 times. 2 – I will do it in another color – 2 is displayed 5 times. 2 is displayed 5 times I make a bar chart, we go up to 5. 2 is displayed 5 times. 3 is displayed 2 times. We have two 3. 4 is shown 1 time here. 5 is not displayed at all. We will not have any height here. Finally, 6 is displayed 1 time. I will make 6 to be displayed 1 time. What I did here is a histogram. This is a histogram here. Very modern word, but I think you’ll agree, that the idea is quite simple. We clarify the frequency of each of these numbers, then we present it with a diagram, and we get a histogram.

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