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?

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.

Explain why the Correct Answer
is the only Correct Answer

Answer 1

[AI-generated answer — Bot GPT 3.5]

The IQR (Interquartile Range) is calculated by finding the difference between the first quartile (Q1) and the third quartile (Q3) of the dataset.

To find the IQR in this dataset:
- Q1 = 2
- Q3 = 4

Therefore, IQR = Q3 - Q1 = 4 - 2 = 2.

The IQR represents the spread of the middle 50% of the data. In this case, it tells us that for the students in the middle 50% of the dataset, there is a range of 2.5 hours in the number of hours spent on the project. This means that the majority of students spent between 2 and 4.5 hours on the project.

Since the IQR is a measure of variability that is not affected by extreme values (like the maximum and minimum), it gives a more accurate representation of the spread of the data in this case.

Answer 2

shorten it

Answer 3

[AI-generated answer — Bot GPT 3.5]

The IQR is 2.5, which means that for the middle 50% of students, there is a range of 2.5 hours in the number of hours spent on the project. This range represents the variability in the time spent by the majority of students.

Answer 4

Which measure of variability—range or IQR—best describes the spread of the dataset?

For a statistics assignment, Shayna randomly surveyed students on how many hours per week they spend playing online games:

1.0 1.0 2.0 6.5 10.0 10.0 10.0 10.0 12.0 12.5 14.0 14.0 14.0 14.0 15.0 15.0 15.5 16.0 17.5 18.0

(1 point)
Responses

IQR; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is skewed, and there are outliers in the dataset.

IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.

Range; the distribution is skewed, and there are outliers in the dataset.
Range; the distribution is skewed, and there are outliers in the dataset.

Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.

Answer 5

[AI-generated answer — Bot GPT 3.5]

IQR; the distribution is skewed, and there are outliers in the dataset.

Explanation:
- In this case, the dataset has a few outliers (values that are far from the rest of the data) such as 6.5, 10, 12, 14, and 18. These outliers can significantly affect the range measure, making it less reliable for describing the spread.
- The IQR is a robust measure of variability that is not influenced by extreme values or outliers, making it the better choice for describing the spread of this skewed dataset with outliers.

Answer 6

Number of goals scored in one season at Whitmore College soccer games follows:

0, 0, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4

Which measure of variability—IQR or MAD— best describes the spread of the dataset?

(1 point)
Responses

MAD; the data distribution is symmetrical
MAD; the data distribution is symmetrical

MAD; the data distribution has outliers
MAD; the data distribution has outliers

IQR; the data distribution is skewed
IQR; the data distribution is skewed

IQR; the data distribution is symmetrical

Answer 7

[AI-generated answer — Bot GPT 3.5]

IQR; the data distribution is skewed

Explanation:
- The dataset provided is not symmetrical as there are more observations towards the higher end of the range (more 3s and 4s).
- The IQR is more suitable for describing the spread of skewed datasets than the MAD (Mean Absolute Deviation) measure.
- Skewed distributions have a more pronounced tail towards one direction, which may lead to inaccurate variability measures when using MAD.

Answer 8

remove the explinations

Answer 9

[AI-generated answer — Bot GPT 3.5]

IQR; the data distribution is skewed

Answer 10

Which measure of variability—range or IQR—best describes the spread of the dataset?

For a statistics assignment, Shayna randomly surveyed students on how many hours per week they spend playing online games:

1.0 1.0 2.0 6.5 10.0 10.0 10.0 10.0 12.0 12.5 14.0 14.0 14.0 14.0 15.0 15.0 15.5 16.0 17.5 18.0

(1 point)
Responses

IQR; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is skewed, and there are outliers in the dataset.

IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.

Range; the distribution is skewed, and there are outliers in the dataset.
Range; the distribution is skewed, and there are outliers in the dataset.

Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.

Answer 11

[AI-generated answer — Bot GPT 3.5]

IQR; the distribution is skewed, and there are outliers in the dataset.