Niran surveyed the students in his class on how many hours they spent on their project Here are the results:
0.5, 1.0, 1.0, 1.0, 1.5, 2.0, 2.0, 2.0, 2.5, 3.0, 3.5, 3.5, 3.5, 4.0, 5.0, 6.0, 8.0, 10
Which of the following is the IQR of the dataset and explains what the value means for this dataset?
(1 point)
The IQR (Interquartile Range) is a measure of statistical dispersion, or how spread out the data is. To calculate the IQR, we first need to find the first quartile (Q1) and the third quartile (Q3).
Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.
In this dataset, when arranged in ascending order:
0.5, 1.0, 1.0, 1.0, 1.5, 2.0, 2.0, 2.0, 2.5, 3.0, 3.5, 3.5, 3.5, 4.0, 5.0, 6.0, 8.0, 10
Q1 = 1.5
Q3 = 4.5
IQR = Q3 - Q1 = 4.5 - 1.5 = 3
Therefore, the IQR of this dataset is 3. This means that the middle 50% of the data falls within a range of 3 hours spent on the project. This can give us an idea of the spread of the data and how much time the majority of students dedicated to their project.