What is the difference between joining the points in a graph and drawing a smooth curve near them?
Those values that haven't actually been measured can be estimated by using a smooth curve versus connecting the points on a graph.
When it comes to representing data on a graph, there are two common approaches: joining the points directly or drawing a smooth curve near them. The choice between these methods depends on the nature of the data and the purpose of the graph.
Joining the points directly involves connecting each data point with a straight line. This method is typically used when the data points represent individual measurements or observations. By connecting the points, you create a visual representation of the individual data points, making it easy to see their distribution and any patterns or trends that may exist. This approach is particularly useful when the data is discrete, meaning there are no data points in between the measured values.
On the other hand, drawing a smooth curve near the points involves fitting a mathematical function to the data and using it to estimate values that haven't been directly measured. This method is typically used when the data points represent a continuous phenomenon and you want to visualize the overall trend rather than the individual values. The smooth curve allows you to capture the general shape or trend of the data, making it easier to make predictions or draw conclusions.
To draw a smooth curve near the points, you can use various techniques such as polynomial regression, moving averages, or spline interpolation. These methods analyze the relationship between the data points and create a curve that best represents the overall trend. The advantage of using a smooth curve is that it can help you visualize the data more accurately, especially when there are irregularities or noise in the measurements.
In summary, joining the points directly with straight lines is appropriate for discrete data points, while drawing a smooth curve near the points is more suitable for continuous data or when you want to estimate values in between the measured points. The choice between these methods depends on the type of data and the specific goals of your analysis or visualization.