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)
Responses

The IQR is 2.5. This means that 2.5 hours is the range of the number of hours spent on the project for 50% of the students.
The IQR is 2.5. This means that 2.5 hours is the range of the number of hours spent on the project for 50% of the students.

The IQR is 2.5. This means that 2.5 hours is the range of the number of hours spent on the project for the middle 50% of the students.
The IQR is 2.5. This means that 2.5 hours is the range of the number of hours spent on the project for the middle 50% of the students.

The IQR is 2.75. This means that 2.75 hours is the range of the number of hours spent on the project for 50% of the students.
The IQR is 2.75. This means that 2.75 hours is the range of the number of hours spent on the project for 50% of the students.

The IQR is 2.75. This means that 2.75 hours is the range of the number of hours spent on the project for the middle 50% of the students.
The IQR is 2.75. This means that 2.75 hours is the range of the number of hours spent on the project for the middle 50% of the students.

1 answer

To determine the Interquartile Range (IQR) of the dataset, we need to first find the first quartile (Q1) and the third quartile (Q3).

The dataset provided is: 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

There are 18 data points.

  1. Finding Q1 (the first quartile): Q1 is the median of the first half of the data (the lower 50%). The first half is: 0.5, 1.0, 1.0, 1.0, 1.5, 2.0, 2.0, 2.0 (8 values) The median of this subset is the average of the 4th and 5th values: Q1 = (1.0 + 1.5) / 2 = 1.25

  2. Finding Q3 (the third quartile): Q3 is the median of the second half of the data (the upper 50%). The second half is: 2.5, 3.0, 3.5, 3.5, 3.5, 4.0, 5.0, 6.0, 8.0, 10 (8 values) The median of this subset is the average of the 4th and 5th values: Q3 = (3.5 + 3.5) / 2 = 3.5

  3. Calculating the IQR: IQR = Q3 - Q1 = 3.5 - 1.25 = 2.25

Now, let's summarize the results:

  • Q1 = 1.25
  • Q3 = 3.5
  • IQR = 2.25

Thus, the correct response is missing. However, if we consider potential options or if there were values slightly off due to typographical errors:

The correct answer I've calculated is not reflected in the given options; you might double-check the data values or the options provided.

If we proceed with your options and no errors were made in the calculations of the quartiles, we conclude that:

  • IQR = 2.25 means that 2.25 hours is the range of the number of hours spent on the project for the middle 50% of the students.

Since 2.25 is not listed, please verify the figures given.