Which measure of variability—range or IQR—best describes the spread of the dataset?
For a statistics assignment, Shayna randomly surveyed students on how many hours per week they spend playing online games:
1.0 1.0 2.0 6.5 10.0 10.0 10.0 10.0 12.0 12.5 14.0 14.0 14.0 14.0 15.0 15.0 15.5 16.0 17.5 18.0
(1 point)
Responses
IQR; the distribution is skewed, and there are outliers in the dataset.
Range; 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.
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.
Number of goals scored in one season at Whitmore College soccer games follows:
0, 0, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4
Which measure of variability—IQR or MAD— best describes the spread of the dataset?
(1 point)
Responses
IQR; the data distribution is symmetrical
MAD; the data distribution has outliers
IQR; the data distribution is skewed
MAD; the data distribution is symmetrical
IQR; the data distribution is skewed.
Based on the given dataset of hours spent playing online games, the measure of variability that best describes the spread of the dataset is the IQR (Interquartile Range) because the distribution is skewed and there are outliers in the dataset. Thus, the correct answer is: IQR; the distribution is skewed, and there are outliers in the dataset.
To determine whether the range or IQR best describes the spread of the dataset, we need to consider the characteristics of the dataset: whether it is skewed or symmetrical, and if there are any outliers present.
To find the range, simply subtract the minimum value from the maximum value. In this case, the minimum value is 1.0 and the maximum value is 18.0. Therefore, the range is 18.0 - 1.0 = 17.0.
To find the IQR (interquartile range), we first need to find the first quartile (Q1) and third quartile (Q3). These quartiles divide the data into four equal parts. To do this, we need to sort the dataset in ascending order:
1.0 1.0 2.0 6.5 10.0 10.0 10.0 10.0 12.0 12.5 14.0 14.0 14.0 14.0 15.0 15.0 15.5 16.0 17.5 18.0
From this sorted dataset, the first quartile (Q1) is the median of the first half of the data, and the third quartile (Q3) is the median of the second half of the data. In this case, Q1 = 10.0 and Q3 = 15.5. Therefore, the IQR is 15.5 - 10.0 = 5.5.
Now we can consider the characteristics of the dataset. We can see that the distribution is skewed to the right, as there are more values towards the lower end and fewer values towards the higher end. Additionally, there are outliers present, such as values 16.0 and 18.0, which are further away from the rest of the data.
Given these characteristics, the best measure of variability to describe the spread of the dataset would be IQR, as it is less influenced by outliers and is better suited for skewed distributions. Therefore, the correct answer is: IQR; the distribution is skewed, and there are outliers in the dataset.