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.