Determine whether the range or interquartile range best describes the spread of a dataset.
The times (in seconds) for a high school boys’ 100-meter race:
11.0 11.2 11.7 12.2 12.4 12.6 12.8 12.9 13.1 13.3 13.8 14.2 14.3 14.3 16.5 17.6 18.0
Responses
IQR; the distribution is skewed, and there are 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.
IQR; the distribution is skewed, and there are outliers in the dataset.
The correct answer is IQR; the distribution is skewed, and there are outliers in the dataset.
To determine whether the range or interquartile range best describes the spread of a dataset, we need to understand these two measures of spread.
The range is the simplest measure of spread. It is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest time is 11.0 seconds, and the largest time is 18.0 seconds. So, the range would be 18.0 - 11.0 = 7.0 seconds.
The interquartile range (IQR) is a measure of spread that focuses on the middle 50% of the dataset. It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1). The first quartile is the value below which 25% of the data falls, and the third quartile is the value below which 75% of the data falls.
To determine which of these measures best describes the spread of the given dataset, we need to consider the characteristics of the distribution and the presence of outliers.
Looking at the given dataset, we can see that the times are not evenly distributed. There is a concentration of times around the 12-second mark, with fewer times at the extremes. This suggests that the distribution may be skewed towards the higher times.
Additionally, there is an outlier in the dataset - the time of 18.0 seconds. This outlier is significantly higher than the rest of the times, and it can impact the measure of spread.
Considering this information, the best description of the spread of this dataset would be "IQR; the distribution is skewed, and there are outliers in the dataset." The interquartile range is a better measure of spread because it is not sensitive to outliers and focuses on the middle 50% of the data, providing a more accurate representation of the typical range of values in the dataset.