Which measure of variability—range or IQR—best describes the spread of the dataset?
Social studies group project grades (out of 100 points) for Mr. Chang’s first period class
85 88 90 90 92 92 95 96 99
(1 point)
Responses
Range; the distribution is skewed, and there are outliers in the dataset.
Range; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
Range; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is symmetrical, or close to it, and there aren't any outliers in the dataset. But don't worry, outliers are just misunderstood data points who wanted to stand out and make a statement. It's always good to have a few clowns in the data circus!
The best measure of variability to describe the spread of the dataset would be the range. In this case, the distribution is not mentioned to be symmetrical or close to being symmetrical, and there are no mentions of outliers. Therefore, the most appropriate choice is "Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset."
To determine whether range or IQR is the better measure of variability to describe the spread of the dataset, we need to consider the characteristics of the data distribution and the presence of outliers.
The range is simply the difference between the highest and lowest values in the dataset. It tells us the extent of the spread but does not provide information about the distribution shape or the other values.
The interquartile range (IQR) is the range covered by the middle 50% of the data. It is calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3). It provides a measure of spread that is not influenced by extreme values or outliers.
In this case, based on the given options, the best choice is "IQR; the distribution is symmetrical, or close to it, and there aren't any outliers in the dataset." This answer assumes that the distribution is symmetrical (or roughly symmetrical) and does not have any outliers. If the dataset meets these criteria, the IQR is a reliable measure of spread.
However, if the distribution is skewed or has outliers, the range would be a better choice. Skewness refers to the asymmetry of the distribution, and outliers are extreme values that do not follow the general pattern of the data. The presence of skewness or outliers can distort the interpretation of the IQR, making the range a more appropriate measure in such cases.
To determine the distribution shape and identify outliers, you can create a histogram or a box plot of the data. These visualizations can give you insights into the data's characteristics and guide you in selecting the appropriate measure of variability.