Question
The shoe size for a varsity field hockey team are: 5.5,5.5,6.0,6.5,6.5,7.0,7.0,7.5,7.5,7.5,8.0,8.0,8.0,8.5,8.5,9.0. Find the IQR and explain how this measure of variability decribe how the dataset varies with a single number.
Answers
GPT 3.5
To find the IQR (Interquartile Range) of the shoe sizes, we first need to find the first quartile (Q1) and the third quartile (Q3).
First, list the data in ascending order: 5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0.
Q1 is the median of the lower half of the data set, which in this case is the median of the first half of the data: (6.5+7.0)/2 = 6.75.
Q3 is the median of the upper half of the data set, which in this case is the median of the second half of the data: (8.0+8.5)/2 = 8.25.
Now, we can calculate the IQR by subtracting Q1 from Q3: 8.25 - 6.75 = 1.5.
The IQR for this dataset is 1.5. The IQR is a measure of how spread out the values in a dataset are. In this case, an IQR of 1.5 means that the middle 50% of the shoe sizes range from 6.75 to 8.25. This single number provides a quick way to understand the spread of the dataset without getting into the details of each individual value.
First, list the data in ascending order: 5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0.
Q1 is the median of the lower half of the data set, which in this case is the median of the first half of the data: (6.5+7.0)/2 = 6.75.
Q3 is the median of the upper half of the data set, which in this case is the median of the second half of the data: (8.0+8.5)/2 = 8.25.
Now, we can calculate the IQR by subtracting Q1 from Q3: 8.25 - 6.75 = 1.5.
The IQR for this dataset is 1.5. The IQR is a measure of how spread out the values in a dataset are. In this case, an IQR of 1.5 means that the middle 50% of the shoe sizes range from 6.75 to 8.25. This single number provides a quick way to understand the spread of the dataset without getting into the details of each individual value.