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?
The IQR (Interquartile Range) of the dataset is the range of the middle 50% of the data. To find the IQR, we first need to find the first quartile (Q1) and the third quartile (Q3).
To find Q1 and Q3, we need to arrange the data 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 is the median of the lower half of the data, which is 2.0
Q3 is the median of the upper half of the data, which is 5.0
Now, we can find the IQR:
IQR = Q3 - Q1 = 5.0 - 2.0 = 3.0
The IQR of the dataset is 3.0. This means that the middle 50% of the data falls within the range of 2.0 hours to 5.0 hours spent on the project. This gives us an idea of the spread of the majority of the data points in the dataset.