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
(1 point)
Responses
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.
IQR; the distribution is skewed, and there are outliers in the dataset.
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 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.
Range; the distribution is skewed, and there are outliers in the dataset.
is this correct?
I apologize for the confusion in my previous response. The correct answer is:
IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
To determine whether the range or interquartile range best describes the spread of a dataset, we need to analyze the distribution and analyze if there are any outliers present.
Looking at the given dataset, the times (in seconds) for a high school boys’ 100-meter race, the values are as follows:
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
First, let's analyze if the distribution is symmetrical or skewed. By observing the data, we can see that the values are not evenly distributed around a central point. There is a cluster of values towards the lower end of the range (11.0 to 13.3) and a few extreme values towards the upper end (16.5, 17.6, 18.0). This indicates that the distribution is skewed.
Next, we need to check for the presence of outliers. In this dataset, the values 16.5, 17.6, and 18.0 are significantly higher than the rest of the values. These can be considered as outliers.
Now, let's determine which measure of spread (range or interquartile range) is more appropriate.
Range is a measure of spread that calculates the difference between the maximum and minimum values in the dataset. In this case, the range would be 18.0 - 11.0 = 7.0 seconds.
Interquartile range (IQR) is a measure of spread that represents the range covered by the middle 50% of the data. It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1).
To calculate the IQR, we need to find the quartiles. The dataset can be ordered in ascending order as follows:
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
The first quartile (Q1) can be found by taking the median of the lower half of the data: (12.6 + 12.8)/2 = 12.7 seconds.
The third quartile (Q3) can be found by taking the median of the upper half of the data: (14.3 + 14.3)/2 = 14.3 seconds.
Now, we can calculate the IQR: IQR = Q3 - Q1 = 14.3 - 12.7 = 1.6 seconds.
Considering the skewed distribution and presence of outliers, the measure of spread that best describes this dataset is the interquartile range (IQR).
Therefore, the correct response is: IQR; the distribution is skewed, and there are outliers in the dataset.