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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 2.75. 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.

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 2.5. 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.

1 answer

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

First, let's 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

Next, we identify the quartiles:

  1. Q1 (first quartile): This is the median of the first half of the data (the lower 50%). The lower half is:

    • 0.5, 1.0, 1.0, 1.0, 1.5, 2.0, 2.0, 2.0 The median of these 8 values (the average of the 4th and 5th values) is:
    • Q1 = (1.0 + 1.5) / 2 = 1.25.

  2. Q3 (third quartile): This is the median of the second half of the data (the upper 50%). The upper half is:

    • 2.5, 3.0, 3.5, 3.5, 3.5, 4.0, 5.0, 6.0, 8.0, 10 The median of these 10 values (the average of the 5th and 6th values) is:
    • Q3 = (3.5 + 4.0) / 2 = 3.75.

  3. IQR (interquartile range): This is calculated as:

    • IQR = Q3 - Q1 = 3.75 - 1.25 = 2.5.

Now, we can interpret the IQR:

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.

Therefore, the correct response is:

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.