5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0
what is the iqr and explane it
To find the interquartile range (IQR) of a dataset, we need to find the first quartile (Q1) and the third quartile (Q3) and then subtract Q1 from Q3.
First, we need to arrange the given dataset in ascending order:
5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0
The dataset has 16 values, so the median (Q2) is the average of the two middle values, in this case, (7.5 + 7.5) / 2 = 7.5.
Now, to find Q1, we need to find the median of the lower half of the dataset, which is from 6.0 to 7.0 (inclusive of both endpoints). The median of this lower half is (6.5 + 6.5) / 2 = 6.5, so Q1 = 6.5.
Similarly, to find Q3, we need to find the median of the upper half of the dataset, which is from 8.0 to 8.5 (inclusive of both endpoints). The median of this upper half is (8.0 + 8.0) / 2 = 8.0, so Q3 = 8.0.
Finally, the interquartile range (IQR) is Q3 - Q1 = 8.0 - 6.5 = 1.5.
Therefore, the IQR of the given dataset is 1.5. The IQR represents the range of the middle 50% of the data, providing a measure of the spread of the dataset that is not influenced by extreme values.
Question
The shoe sizes for a varsity field hockey team are: 5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0 Which of the following is the IQR and explains how this measure of variability describes how the values of a dataset vary with a single nu (1 point) The IQR is 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other. The IQR is 3.5.This means that the shoe sizes for half of the players are within 3.5 shoe sizes of each other. The IQR is 1.5. This means that the shoe sizes for half of the players are within 1.5 shoe sizes of each other. The IQR is 3.5. This means that the shoe sizes for the middle half of the players are within 3.5 shoe sizes of each other.
The shoe sizes for a varsity field hockey team are: 5.5, 5.5, 6.0, 6.5, 6.5, 7.0, 7.0, 7.5, 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 8.5, 9.0 Which of the following is the IQR and explains how this measure of variability describes how the values of a dataset vary with a single nu (1 point) The IQR is 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other. The IQR is 3.5.This means that the shoe sizes for half of the players are within 3.5 shoe sizes of each other. The IQR is 1.5. This means that the shoe sizes for half of the players are within 1.5 shoe sizes of each other. The IQR is 3.5. This means that the shoe sizes for the middle half of the players are within 3.5 shoe sizes of each other.
The correct answer is: The IQR is 1.5. This means that the shoe sizes for the middle half of the players are within 1.5 shoe sizes of each other.
The Interquartile Range (IQR) is a measure of variability that describes how the values in a dataset vary. It specifically looks at the range of the middle 50% of the data, indicating the spread of values that are more representative of the overall data distribution. In this case, an IQR of 1.5 suggests that the shoe sizes for the middle half of the players are within a range of 1.5 shoe sizes of each other. This means that the shoe sizes are relatively consistent within this middle portion of the dataset.
This dataset represents the number of likes Julia had on her last 10 Instagram posts:
Which of the following is the MAD of the dataset and explains what the value means or this dataset? (1 point) The MAD is 13 . This means the number of likes differ, on average, by 13 from the mean of 27.5 likes. The MAD is 6 . This means the number of likes differ by 6 from the mean of 27.5 likes. The MAD is 6 . This means the number of likes differ, on average, by 6 from the mean of 27.5 likes. The MAD is 13 . This means the number of likes differ by 13 from the mean of 27.5 likes.
The correct answer is: The MAD is 6. This means the number of likes differ, on average, by 6 from the mean of 27.5 likes.
The Mean Absolute Deviation (MAD) is a measurement of the average difference between each data point and the mean. In this case, an MAD of 6 means that, on average, the number of likes on Julia's Instagram posts deviates by 6 from the mean number of likes, which is 27.5. This suggests that the variability in the number of likes Julia receives on her posts is relatively consistent, with most values falling within 6 likes above or below the mean.
This dataset represents the number of likes Julia had on her last 10 Instagram posts: \[ 17,19,21,23,28,31,31,34,35,36 \] Which of the following is the MAD of the dataset and explains what the value means for this dataset? (1 point) The MAD is 13. This means the number of likes differ, on average, by 13 from the mean of 27.5 likes. The MAD is 13. This means the number of likes differ by 13 from the mean of 27.5 likes. The MAD is 6 . This means the number of likes differ by 6 from the mean of 27.5 likes. The MAD is 6 . This means the number of likes differ, on average, by 6 from the mean of 27.5 likes. In
The correct answer is: The MAD is 6. This means the number of likes differ by 6 from the mean of 27.5 likes.
In this dataset, the Mean Absolute Deviation (MAD) measures the average absolute difference between each data point and the mean of the dataset, which is 27.5 in this case. An MAD of 6 indicates that, on average, the number of likes on Julia's Instagram posts differs by 6 from the mean of 27.5 likes. This means that the variability in the number of likes Julia receives on her posts is relatively consistent, with most values falling within 6 likes above or below the mean.
can you show work on how you got 6 as the MAD
To calculate the Mean Absolute Deviation (MAD) for the dataset \[17, 19, 21, 23, 28, 31, 31, 34, 35, 36\]:
1. Find the Mean:
Sum all the numbers in the dataset and divide by the total number of values:
\[ \text{Mean} = \frac{17+19+21+23+28+31+31+34+35+36}{10} = \frac{275}{10} = 27.5 \]
2. Find the Absolute Deviation for each value:
Subtract the mean from each individual value, and take the absolute value of the difference:
\[ |17-27.5| = 10.5 \]
\[ |19-27.5| = 8.5 \]
\[ |21-27.5| = 6.5 \]
\[ |23-27.5| = 4.5 \]
\[ |28-27.5| = 0.5 \]
\[ |31-27.5| = 3.5 \]
\[ |31-27.5| = 3.5 \]
\[ |34-27.5| = 6.5 \]
\[ |35-27.5| = 7.5 \]
\[ |36-27.5| = 8.5 \]
3. Find the Average Absolute Deviation:
Add up all the absolute deviations and divide by the total number of values:
\[ \text{MAD} = \frac{10.5+8.5+6.5+4.5+0.5+3.5+3.5+6.5+7.5+8.5}{10} = \frac{59.5}{10} = 5.95 \]
Therefore, the Mean Absolute Deviation (MAD) for the dataset is approximately 5.95 or rounded to 6.
Determine whether the range or interquartile range best describes the spread of a dataset.
The times (in seconds) for a high school boys’ 100-meter race:
11.0 11.2 11.7 12.2 12.4 12.6 12.8 12.9 13.1 13.3 13.8 14.2 14.3 14.3 16.5 17.6 18.0
(1 point)
Responses
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.
Range; 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.
IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
IQR; the distribution is skewed, and there are outliers in the dataset.