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ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to see how useful a histogram can be when you need to show a bunch of data in an easy to read format. Also, learn how you can easily gather the information you need from looking at a histogram.

In math, a **histogram** is a visual way to display frequency data using bars. A feature of histograms is that they show the frequency of continuous data, such as the number of trees at various heights from 3 feet to 8 feet. They are not used to show categorical data, such as the population of dogs in Norway, Finland, and Sweden. Another feature of histograms is that the data can be grouped into ranges. For example, the height of the trees can be grouped into 3 to 4 feet, 5 to 6 feet, and 7 to 8 feet.

How do you know when to use a histogram? You can decide this by looking at your data. Ask yourself, 'Is the data continuous, or can I group the data into ranges?'

What you are looking for is a group of data that is **continuous**. What this means is that the data covers a range of values that does not jump. For example, the range of tree heights is 3 to 8 feet. The data does not jump from 4 to 6 feet. There is no gap. The countries of Norway, Finland, and Sweden, though, do jump. There is no continuity between the countries. They are separate entities. For histograms, you need continuous information and not just categories that jump.

Histograms are great at showing results, such as the frequency of the number of trees at various heights from 3 to 8 feet. So, if you have a set of continuous data, then you can use a histogram to show the results visually.

So, let's say that I surveyed a hill by my house, and I counted the number of trees at various heights. I found that at 3 feet, my hill only had 2 trees. At 4 feet, my hill had 4 trees. At 5 feet, I only had 1 tree. At 6 feet, I had 7 trees. At 7 feet, it was 8 trees. Then at 8 feet, I had 2 trees. The histogram for this information would have the *x-axis* showing the range of heights from 3 to 8 feet. Then, the *y-axis* would have the number of trees.

Then, I have several options for showing the data. I can show the data for each height separately, or I can group them into ranges, such as 3 to 4 feet, 5 to 6 feet, and then 7 to 8 feet.

I can combine the data into any number of different ranges. I can also group them into ranges, such as 3 to 5 feet and 6 to 8 feet. It is your choice based on the kind of information you want to show. If you want to be specific, then use smaller ranges or don't use ranges at all. If you want to be more general with your data and just show an overview, then you can use larger ranges to group your data.

To create the histogram below, what I have done for every tree measured is increase that tree height's bar on the histogram by 1. So, if my tree measures 3 feet, then I increase the bar for 3 feet by 1. After measuring 2 trees that are both 3 feet high, my bar at 3 feet should be at the number 2, since there are 2 trees that are 3 feet high. I continue doing this until I have all of my data on the histogram.

By looking at the tree height histogram, I can tell how many trees are in each data range. For example, for the tree height histogram that shows each height, I see that I have 2 trees that are 3 feet high and 7 trees that are 6 feet high.

Reading a histogram is fairly straightforward. The *y-axis* tells you the frequency of the data. By looking at the whole thing, I can get a sense of which part of the data is more popular or is more important for answering my question. For the tree height histogram, I see that my hill contains the most trees that are 7 feet high. So, I can say that on my hill, 7-foot trees are more common than trees of other heights.

A **histogram** is a visual way to show the frequency of data using bars. The histogram's data must be **continuous**. It cannot have a jump in it or be categorical. The data can be grouped into ranges for more general data. The bar shows the frequency of each data point or range.

To create a histogram, you increase the bar for each data point or range by 1 whenever you see data at that point or range occur. For example, when I see a tree with a height of 4 feet, I increase the bar at 4 feet by 1 to account for this particular piece of data.

To read a histogram is a matter of looking at the bar, then at the *x-axis* to see what the data represents, then looking at the *y-axis* to see how often that particular data occurs. For the tree height histogram, if the bar at 7 feet goes up to 8 on the *y-axis*, it means that I have 8 trees that are 7 feet high.

Following this video lesson, you should be able to:

- Define histogram and explain when you should use one
- Explain how to create and how to read a histogram

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ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

- Statistical Analysis with Categorical Data 5:20
- Understanding Bar Graphs and Pie Charts 9:36
- Summarizing Categorical Data using Tables 4:57
- How to Calculate Percent Increase with Relative & Cumulative Frequency Tables 5:47
- What is a Two-Way Table? 3:40
- Make Estimates and Predictions from Categorical Data 3:13
- What is Quantitative Data? - Definition & Examples 4:11
- What is a Histogram in Math? - Definition & Examples 5:12
- How to Calculate Mean, Median, Mode & Range 8:30
- Describing the Relationship between Two Quantitative Variables 4:44
- Reading and Interpreting Line Graphs 6:09
- Making Estimates and Predictions using Quantitative Data 4:07
- Go to ELM Test - Numbers and Data: Data & Statistics

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