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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Nick Rogers*

An ogive plot is useful in statistics when we want to know how many observations to expect for a range of data. It allows us to quickly see how many observations were measured for all ranges less than a particular number.

In statistics, frequencies are very important. Statisticians use plots to illustrate data in pictorial form to make it easier to understand. If you like drawing pictures and making plots, you just might find statistics to be a lot of fun!

Do you know what **cumulative** means? According to one definition, it means ''by successive additions.'' If you know how to add, then you can use that skill to construct graphs called **cumulative frequency plots**, which are also known as **ogive plots**. By the time you finish this lesson, you'll be ready to go out and collect your own data and make some beautiful graphs!

An **ogive graph** is a plot used in statistics to show cumulative frequencies. It allows us to quickly estimate the number of observations that are less than or equal to a particular value. Let's consider an example, and construct both a frequency and ogive plot to see the difference.

Suppose that we conducted an experiment on people between the ages of 0 and 30 and recorded some data for some age ranges. We could place these values in a table. In the table, we would write down the average value for each of six ranges of the ages we have surveyed. In a third column, we would write down the sum of all of our observations up to and including that age.

Range | Value | Sum |
---|---|---|

0-5 | 2 | 2 |

6-10 | 3 | 5 |

11-15 | 2 | 7 |

16-20 | 4 | 11 |

21-25 | 5 | 16 |

26-30 | 1 | 17 |

In this example, people in the age range 0-5 had a value of 2, and people aged 6-10 had a value of 3. The third column tells us the sum of observations for people below the upper limit of the age for that column. Therefore, in our experiment, we found that all people below the age of 10 had a total value of 5, while everyone (all of those below age 30) had a total value of 17.

A **frequency plot** like the one on top in this image would show the frequency of observations (or the value) for each age range. We construct this type of graph by placing the age ranges on the horizontal, or x-axis, and plotting bars with heights equal to the observations above each range. An ogive plot, shown on the bottom of the image, shows the values in the third column of our table - namely, the cumulative frequencies.

An ogive is different from a frequency plot because it's usually drawn using straight line segments instead of vertical bars. Is each consecutive value always higher than the ones before it? Yes! This is because the values for the ogive graph are obtained by adding up all of the observations so far.

Suppose that we're given an ogive plot and we want to know how many observations lie within a particular range. For example, how many observations do we expect between 16 and 25? We can use the given ogive plot to go backwards and recover the original information. The ogive plot tells us that there were 16 observations less than 25 and 7 observations less than 15. Therefore, we know that between 16 and 25, there must be 16 - 7 = 9 observations.

In this lesson, you learned what an **ogive graph** is and how to create one of your own. You also learned how to think about the meaning of the data represented, and how to recreate the original set of observations if you're presented with only an **ogive plot**, which is also known as a **cumulative frequency plot**.

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Math for Kids23 chapters | 325 lessons

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