Use the image to answer the question. What is the median of the box plot? (1 point) Responses 95 95 97 97 91 91 99
The median of the box plot is 95.
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 2.5. 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. 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. Skip to navigation
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.
Of the mean, median, and mode, which measure of center is most affected by outliers? Explain your reasoning including an example with at least 10 data points.(4 points)
The measure of center that is most affected by outliers is the mean. The mean is calculated by adding up all the values and then dividing by the number of values. Outliers can heavily impact the mean because they can significantly change the total sum of the data, pulling the average towards the extreme value of the outlier.
For example, let's consider a dataset of the following numbers: 10, 11, 12, 13, 14, 15, 16, 17, 18, 100.
If we calculate the mean of this dataset:
(10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 100) / 10 = 16.6
The mean of this dataset is 16.6. However, we have one outlier, which is 100. If we remove this outlier and recalculate the mean, it will be:
(10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18) / 9 = 14.33
As we can see, the outlier value of 100 significantly affected the mean of the dataset, pulling it higher.
In contrast, the median and mode are less affected by outliers because they are more resistant to extreme values. The median is the middle value when the data is arranged in numerical order, and the mode is the value that appears most frequently in the dataset. These measures are not influenced as much by outliers because they do not consider the actual values of the data points, but rather their position or frequency.