Vivian surveyed bicyclists in her community to see the average number of miles they biked per day. Her results are shown below.
7, 10, 13, 4, 12, 21, 10, 3
What is the MAD of her data set? What does this tell you about the number of miles biked each day by the bicyclists?
The mean of the data set is ? .
The MAD of the data set is ? .
So, the number of miles biked each day by the bicyclists varied by an average of ? miles from the mean.
To find the mean of the data set, we add up all the numbers and divide by the total number of values:
Mean = (7 + 10 + 13 + 4 + 12 + 21 + 10 + 3) ÷ 8
Mean = 80 ÷ 8
Mean = 10
The mean number of miles biked per day by the bicyclists is 10.
To find the MAD of the data set, we first need to find the absolute deviations from the mean. We subtract the mean from each value and take the absolute value:
|7 - 10| = 3
|10 - 10| = 0
|13 - 10| = 3
|4 - 10| = 6
|12 - 10| = 2
|21 - 10| = 11
|10 - 10| = 0
|3 - 10| = 7
Next, we find the mean of these absolute deviations:
MAD = (3 + 0 + 3 + 6 + 2 + 11 + 0 + 7) ÷ 8
MAD = 32 ÷ 8
MAD = 4
The MAD of the data set is 4.
This tells us that on average, the number of miles biked each day by the bicyclists varied by 4 miles from the mean of 10. This means that there is some variability in the distances biked by different individuals in the group. Some might bike much more or much less than the average of 10 miles per day.
So it would be
The MAD of the data set is 4. Am I correct?
Yes, that is correct!
So for this one it would be like this
So, the number of miles biked each day by the bicyclists varied by an average of 7 miles from the mean.
Actually, the MAD of the data set in your previous question was 4, so the correct sentence would be:
So, the number of miles biked each day by the bicyclists varied by an average of 4 miles from the mean.
Sorry for any confusion caused!
Tahnks!
You're welcome! Don't hesitate to ask if you have any more questions.
Ok/...
Wyatt analyzed the data from his science experiment and found that the MAD was greater than the IQR.
What does this tell you about the variability of the data?
A. The middle 50% of the data is spread out more than the average variation.
B. The average variation is spread out more than the middle 50% of the data.
C.The average of the data is closer to the least value than it is to the greatest value.
D. The average of the data is closer to the greatest value than it is to the least value.
Which is the correct answer??
The correct answer is B.
When the MAD is greater than the IQR, it means that there is more variability in the data outside of the middle 50% of the values (which is represented by the IQR). This indicates that the average variation (as measured by the MAD) is spread out more than the middle 50% of the data.
YAYAYA!!!!!
Great, glad to hear that! Is there anything else you need help with?
Hui recorded the temperature at the same time each day for one month. He found that the MAD for his data set was 4.3.
Use this information to select all the true statements about the temperatures that Hui recorded.
A. The lowest temperature varied only 4.3 degrees from the mean.
B. On most days, the temperature varied about 4.3 degrees from the mean.
C. No temperature varied more than 4.3 degrees from the mean.
D. The highest temperature varied about 4.3 degrees from the lowest temperature.
E. Temperatures generally increased or decreased by about 4.3 degrees from the mean.
The correct statement is:
B. On most days, the temperature varied about 4.3 degrees from the mean.
Option A is incorrect because the MAD tells us about the variability around the mean, not necessarily the variability between the lowest temperature and the mean.
Option C is incorrect because the MAD tells us about the average absolute deviation from the mean. It is possible that some temperatures could vary more than 4.3 degrees from the mean.
Option D is incorrect because we don't have enough information to make a statement about the highest temperature varying a certain number of degrees from the lowest temperature.
Option E is also incorrect because the fact that the MAD is 4.3 does not necessarily imply that temperatures generally increased or decreased by about 4.3 degrees from the mean.
So there is only 1 answer/???
Yes, that's correct. Answer B is the only true statement based on the information given.
Ok... I guess.s...
If you have any questions or doubts, please let me know and I will be happy to help.
Natalia recorded daily visitors to her new website. The data for the first 9 days is shown below.
25, 31, 27, 33, 41, 39, 48, 46, 52
Natalia is curious to know the MAD and the IQR for her visitor data.
Identify each of these two measures of variability for the data by dragging a number to each box.
6 7 8 9 1 6 1 7 1 8 1 9
MAD IQR
Using the data given:
MAD = 6
IQR = 15
So the correct answer is:
MAD: 6
IQR: 15
You can drag the numbers to the boxes as follows:
6 -> MAD
15 -> IQR
Please note that the IQR is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1). In this case, Q1 is the median of the first four values (25, 31, 27, 33), which is 28. Q3 is the median of the last four values (48, 46, 52, 39), which is 47. So the IQR is 47 - 28 = 15.
Wait but there is no 15.... to put as IQR (I think something is offf)
I'm sorry for the confusion. You are correct - there is no 15 in the list of numbers provided, so I made an error.
To find the IQR, we first need to find the median of the data set.
Natalia's data set consists of 9 values, so the median is the middle value when the numbers are put in order. First, we put these numbers in order from smallest to largest:
25, 27, 31, 33, 39, 41, 46, 48, 52
The median is the middle value of this ordered list, which is 39.
Next, we find the first quartile (Q1), which is the median of the lower half of the data (all values less than or equal to 39):
25, 27, 31, 33, 39
The median of this lower half of the data set is 31.
Finally, we find the third quartile (Q3), which is the median of the upper half of the data (all values greater than or equal to 39):
39, 41, 46, 48, 52
The median of this upper half of the data set is 46.
The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 46 - 31 = 15.
So the correct answer is:
MAD: 6
IQR: 15
NO THE IQR IS WRONG!!!!!!!!!!!!!!!!!!!!!!!!!
You're right, I apologize for the mistake in my previous message.
To calculate the IQR, we need to first find the median of the entire dataset. Since there are 9 values in the dataset, the median will be the average of the two middle values, which in this case is (39 + 41)/2 = 40.
Next, we need to find the first quartile (Q1), which is the median of the lower half of the dataset. The lower half of the dataset is from 25 to 39, so we need to find the median of this half. Since there are 5 values in this half, the median will be the middle value, which is 31.
Similarly, we need to find the third quartile (Q3), which is the median of the upper half of the dataset. The upper half of the dataset is from 41 to 52, so we need to find the median of this half. Since there are 5 values in this half, the median will be the middle value, which is 48.
The IQR is the difference between the third quartile (Q3) and the first quartile (Q1), so in this case:
IQR = Q3 - Q1 = 48 - 31 = 17
So the correct answer is:
MAD: 6
IQR: 17