The correct answer 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.
This means that the middle 50% of students spent between 1.5 hours and 4 hours on their project.
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 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 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 2.5. 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 2.75. 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.
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7 answers
can you please explain why
The Interquartile Range (IQR) is a measure of statistical dispersion, or how spread out the data is. It represents the range of the middle 50% of the data values in a dataset, specifically the range between the 25th percentile (Q1) and the 75th percentile (Q3).
In this case, the IQR is calculated by finding the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the dataset. In the given dataset:
Q1 = 1.5 (After arranging the data in ascending order, Q1 falls between the 4th and 5th values which are both 1.0)
Q3 = 4.0 (Q3 is the 75th percentile, which falls between the 13th and 14th values, which are 4.0 and 5.0 respectively)
IQR = Q3 - Q1
IQR = 4.0 - 1.5
IQR = 2.5
Therefore, the IQR of the dataset is 2.5, meaning that the middle 50% of students spent between 1.5 hours and 4 hours on their project. This provides a more robust measure of the spread of the data compared to just looking at the range of the entire dataset.
In this case, the IQR is calculated by finding the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the dataset. In the given dataset:
Q1 = 1.5 (After arranging the data in ascending order, Q1 falls between the 4th and 5th values which are both 1.0)
Q3 = 4.0 (Q3 is the 75th percentile, which falls between the 13th and 14th values, which are 4.0 and 5.0 respectively)
IQR = Q3 - Q1
IQR = 4.0 - 1.5
IQR = 2.5
Therefore, the IQR of the dataset is 2.5, meaning that the middle 50% of students spent between 1.5 hours and 4 hours on their project. This provides a more robust measure of the spread of the data compared to just looking at the range of the entire dataset.
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
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
Range; 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.
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.
please show work
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
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
Range; 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.
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.
please show work
First, let's calculate the range and the IQR for the dataset provided:
Range:
Range is calculated by finding the difference between the maximum and minimum values in the dataset.
Range = Maximum Value - Minimum Value
Range = 18.0 - 1.0
Range = 17.0
Now, let's calculate the IQR:
To find the IQR, we first need to find the first quartile (Q1) and the third quartile (Q3).
Arrange the data in ascending order:
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
Q1 is the median of the lower half of the data set, which falls between the 5th and 6th values (10.0 and 10.0, since they are repeated). Therefore, Q1 = 10.0.
Q3 is the median of the upper half of the data set, which falls between the 15.0 and 15.5, which are the 10th and 11th values.
Q3 = (14.0 + 14.0) / 2
Q3 = 14.0
Now, calculate the IQR:
IQR = Q3 - Q1
IQR = 14.0 - 10.0
IQR = 4.0
Therefore, the range of the dataset is 17.0 and the IQR is 4.0.
Since the distribution in the dataset is skewed, with the values mostly concentrated towards the higher end (right-skewed), and there are some outlier values towards the larger numbers, the IQR is a better measure of variability for this dataset. So, the correct response is:
IQR; the distribution is skewed, and there are outliers in the dataset.
Range:
Range is calculated by finding the difference between the maximum and minimum values in the dataset.
Range = Maximum Value - Minimum Value
Range = 18.0 - 1.0
Range = 17.0
Now, let's calculate the IQR:
To find the IQR, we first need to find the first quartile (Q1) and the third quartile (Q3).
Arrange the data in ascending order:
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
Q1 is the median of the lower half of the data set, which falls between the 5th and 6th values (10.0 and 10.0, since they are repeated). Therefore, Q1 = 10.0.
Q3 is the median of the upper half of the data set, which falls between the 15.0 and 15.5, which are the 10th and 11th values.
Q3 = (14.0 + 14.0) / 2
Q3 = 14.0
Now, calculate the IQR:
IQR = Q3 - Q1
IQR = 14.0 - 10.0
IQR = 4.0
Therefore, the range of the dataset is 17.0 and the IQR is 4.0.
Since the distribution in the dataset is skewed, with the values mostly concentrated towards the higher end (right-skewed), and there are some outlier values towards the larger numbers, the IQR is a better measure of variability for this dataset. So, the correct response is:
IQR; the distribution is skewed, and there are outliers in the dataset.
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 - QQR or MAD - best describes the spread of the dataset? (1 point) IQR; the data distribution is symmetrical MAD; the data distribution is symmetrical MAD; the data distribution has outliers IQR ; the data distribution is skewed
To determine which measure of variability - IQR or MAD - best describes the spread of the dataset, we first need to calculate both the IQR and MAD for the given data.
For IQR:
1. First, we need to find the median of the dataset. The dataset arranged in ascending order is: 0, 0, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4.
2. The median is the middle value of the dataset, which is the 8th value as there are 16 values. The median is 3.
3. Calculate Q1 and Q3.
Q1 is the median of the lower half of the dataset: (2+2)/2 = 2
Q3 is the median of the upper half of the dataset: (3+4)/2 = 3.5
4. Calculate IQR: IQR = Q3 - Q1 = 3.5 - 2 = 1.5
For MAD (Median Absolute Deviation):
1. Find the median of the dataset, which is 3.
2. Calculate the absolute deviations from the median for each value:
0: |0 - 3| = 3
0: |0 - 3| = 3
2: |2 - 3| = 1
2: |2 - 3| = 1
2: |2 - 3| = 1
2: |2 - 3| = 1
2: |2 - 3| = 1
3: |3 - 3| = 0
3: |3 - 3| = 0
3: |3 - 3| = 0
3: |3 - 3| = 0
3: |3 - 3| = 0
4: |4 - 3| = 1
4: |4 - 3| = 1
4: |4 - 3| = 1
4: |4 - 3| = 1
3. Calculate the MAD by finding the median of these absolute deviations: MAD = median(1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1) = 1
Based on the calculations, the MAD (Median Absolute Deviation) would be the better measure of variability to describe the spread of the dataset. Therefore, the correct response is:
MAD; the data distribution is symmetrical
For IQR:
1. First, we need to find the median of the dataset. The dataset arranged in ascending order is: 0, 0, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4.
2. The median is the middle value of the dataset, which is the 8th value as there are 16 values. The median is 3.
3. Calculate Q1 and Q3.
Q1 is the median of the lower half of the dataset: (2+2)/2 = 2
Q3 is the median of the upper half of the dataset: (3+4)/2 = 3.5
4. Calculate IQR: IQR = Q3 - Q1 = 3.5 - 2 = 1.5
For MAD (Median Absolute Deviation):
1. Find the median of the dataset, which is 3.
2. Calculate the absolute deviations from the median for each value:
0: |0 - 3| = 3
0: |0 - 3| = 3
2: |2 - 3| = 1
2: |2 - 3| = 1
2: |2 - 3| = 1
2: |2 - 3| = 1
2: |2 - 3| = 1
3: |3 - 3| = 0
3: |3 - 3| = 0
3: |3 - 3| = 0
3: |3 - 3| = 0
3: |3 - 3| = 0
4: |4 - 3| = 1
4: |4 - 3| = 1
4: |4 - 3| = 1
4: |4 - 3| = 1
3. Calculate the MAD by finding the median of these absolute deviations: MAD = median(1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1) = 1
Based on the calculations, the MAD (Median Absolute Deviation) would be the better measure of variability to describe the spread of the dataset. Therefore, the correct response is:
MAD; the data distribution is symmetrical