Question

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)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The IQR (Interquartile Range) is a measure of statistical dispersion, or in simpler terms, it measures how spread out the values in a dataset are.

To calculate the IQR, we first need to find the first quartile (Q1) and 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 we arrange the hours spent on the project 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 = 1.0 (average of the two middle values: 1.0 and 1.0)
Q3 = 4.0 (average of the two middle values: 4.0 and 5.0)

IQR = Q3 - Q1
IQR = 4.0 - 1.0
IQR = 3.0

The IQR of this dataset is 3.0. This means that the middle 50% of the data (between Q1 and Q3) is spread out over a range of 3 hours. This can be interpreted as the typical range of hours spent on the project by most students in the class.