Hi there! The statistical investigative process is used to solve problems with data and variation, which means it helps us analyze data that varies from one item to the next. This is different from math problems that usually involve solving equations.

Let’s look at an example to understand the difference between data with and without variation. Suppose you wanted to know the average height of a group of people. If all the people in the group were the same height, then there would be no variation in the data, and you could simply add up all their heights and divide by the number of people to find the average. This would be a simple math problem.

However, in the real world, people’s heights vary, and you would need to use the statistical investigative process to find the average height of the group. You would start by asking a question, such as “What is the average height of the people in this group?” Then, you would collect data by measuring the height of each person in the group.

Next, you would analyze the data by looking for patterns and relationships between the different heights. You might find that some people are taller and some are shorter, and you would need to account for this variation in your calculations.

Finally, you would interpret the results by drawing conclusions from your analysis. You might find that the average height of the group is 5 feet 7 inches, which would be an important piece of information if you were, for example, designing clothing or furniture for this group of people. Check out the table below for more examples of data with and without variation.

Data with Variation |
Data without Variation |

The heights of a group of people | The length of a piece of wood |

The number of goals scored by different soccer players in a season | The weight of a bag of sugar |

The grades of students in a class | The number of chairs in a room |

The daily temperature in a city over a month | The distance between two points |

The prices of different cars in a dealership | The price of a single item |

As you can see, data with variation refers to data where the values differ from one item to the next. This type of data requires the statistical investigative process to analyze and draw conclusions from it. Data without variation, on the other hand, has the same value for each item, and is more suited for simple math problems. Understanding the difference between data with and without variation is important to know when it comes to data analysis and problem-solving.