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Math for Kids23 chapters | 325 lessons

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Instructor:
*Nick Rogers*

Frequency histograms are a type of graph that allows us to easily compare categories or ranges of data. They are easy to read and construct and can be a great tool for you to display statistics.

Have you ever seen a histogram? A **histogram** is a popular graph used in statistics. The vertical axis shows how much of something that you have, and the horizontal axis labels the categories that you are plotting. For example, if your class consisted of 12 boys and 10 girls, you'd plot a histogram of the students as follows:

On the left of the diagram is a traditional histogram: it displays the number of boys and girls in the class. To the right is the same data plotted as a frequency histogram. You calculate the frequencies by comparing the number of boys and girls to the total number of students. How can you calculate the frequency of girls and boys in the class? You can do this by using fractions of the total number of students. There are 12 boys and 10 girls, so there are 22 students total.

Let's calculate the frequencies:

- Girls / Students = 10 / 22
- Girls / Students = 0.45
- Boys / Students = 12 / 22
- Boys / Students = 0.54

Therefore, the frequency of girls in the class is 0.45 or about 45%. Similarly, the frequency of boys is 0.54 or 54%. It is very useful to consider frequencies when drawing these kinds of graphs because frequency is never more than '1.' What other kinds of things can you measure with these plots? Almost anything!

Let's try to make some plots using data. Imagine that you asked everyone in your class what their favorite color is. You collect all of the answers in a list:

(blue, yellow, green, blue, red, blue, yellow, green, blue, red, green, blue, red, blue, yellow, yellow, green, blue, blue, red, purple, orange)

This list is a little hard to read, so one way we can make it easier to understand is to arrange it into a nice table:

Color | Number | Frequency |
---|---|---|

Blue | 8 | 0.36 |

Red | 4 | 0.18 |

Yellow | 4 | 0.18 |

Green | 4 | 0.18 |

Purple | 1 | 0.18 |

Orange | 1 | 0.045 |

Now that we can see all of the data in a table, we find that blue is the most popular color, followed by red, yellow, and green; purple and orange were the least popular. This certainly helps our understanding, but can you create a histogram from this data? A histogram may look like this:

What would you change to convert this histogram into a frequency histogram? If you think that the y-axis labels should change, you are correct and well on your way to creating your own frequency histogram plots!

Sometimes data can look very predictable and sometimes it is harder to understand. Take a look at these two types of data:

The left is what we call a **multimodal** or asymmetric distribution. This means that it lacks symmetry. The data to the right is **symmetric**, which means that there is a common answer and equal amounts above and below that answer. If you draw a line down the middle of this graph, it would look the same on both sides.

In this lesson, you learned how to calculate frequencies from data and discovered how to create your own **histogram**. You should now be able to decide if data is **symmetric** or **multimodal**.

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Math for Kids23 chapters | 325 lessons

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- Frequency Definition: Lesson for Kids
- How to Make a Frequency Distribution Table 3:57
- What is a Frequency Distribution Table? - Definition & Example 3:05
- How to Make a Frequency Histogram
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