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The shoe sizes 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,...Question
The shoe sizes 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
Which of the following is the IQR and explains how this measure of variability describes how the values of a dataset vary with a single number?
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
Which of the following is the IQR and explains how this measure of variability describes how the values of a dataset vary with a single number?
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GPT 3.5
To find the IQR (interquartile range) of the given dataset, we need to first find the first quartile (Q1) and the third quartile (Q3).
1) Arrange 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
2) Find Q1:
To find Q1, we need to locate the median of the lower half of the data, which is the value separating the first 25% of the data from the remaining 75%. In this case, the lower half consists of the first 8 values:
5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5
The median of this lower half is the average of the numbers in the middle: (6.5 + 7.0) / 2 = 6.75.
Therefore, Q1 = 6.75.
3) Find Q3:
Similarly, to find Q3, we need to locate the median of the upper half of the data, which is the value separating the first 75% of the data from the remaining 25%. In this case, the upper half consists of the last 8 values:
7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0
The median of this upper half is the average of the numbers in the middle: (8.0 + 8.5) / 2 = 8.25.
Therefore, Q3 = 8.25.
4) Calculate the IQR:
The IQR is found by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 8.25 - 6.75 = 1.5.
The IQR, 1.5, represents the range between the first quartile (Q1) and the third quartile (Q3). It describes how the middle 50% of the data is spread out. In this case, it means that half of the shoe sizes fall within a range of 1.5 units, ranging from 6.75 to 8.25. This measure of variability is useful because it summarizes the spread of the middle portion of the dataset into a single number, allowing for a concise understanding of how values are distributed within that range.
1) Arrange 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
2) Find Q1:
To find Q1, we need to locate the median of the lower half of the data, which is the value separating the first 25% of the data from the remaining 75%. In this case, the lower half consists of the first 8 values:
5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5
The median of this lower half is the average of the numbers in the middle: (6.5 + 7.0) / 2 = 6.75.
Therefore, Q1 = 6.75.
3) Find Q3:
Similarly, to find Q3, we need to locate the median of the upper half of the data, which is the value separating the first 75% of the data from the remaining 25%. In this case, the upper half consists of the last 8 values:
7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0
The median of this upper half is the average of the numbers in the middle: (8.0 + 8.5) / 2 = 8.25.
Therefore, Q3 = 8.25.
4) Calculate the IQR:
The IQR is found by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 8.25 - 6.75 = 1.5.
The IQR, 1.5, represents the range between the first quartile (Q1) and the third quartile (Q3). It describes how the middle 50% of the data is spread out. In this case, it means that half of the shoe sizes fall within a range of 1.5 units, ranging from 6.75 to 8.25. This measure of variability is useful because it summarizes the spread of the middle portion of the dataset into a single number, allowing for a concise understanding of how values are distributed within that range.
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