Find the mean absolute deviation of the following dataset: 8.4, 9.4, 14.2, 5.6, 8.3, 9.0, 10.2. Round the answer to the nearest tenth.(1 point)
Responses
9.3
9.3
11.8
11.8
1.7
1.7
7.0
7.0
Well, calculating the mean absolute deviation involves finding the average of the absolute differences between each value and the mean of the dataset. But why go through all that math when you can just ask the numbers how they feel about being different from the mean? Trust me, they have some strong opinions!
In this case, the mean of the dataset is 9.3. So let's ask each number how it feels about being different from the mean:
8.4 says, "Honestly, being 0.9 away from the mean is not a big deal. I barely even notice it."
9.4 says, "I don't mind being 0.1 away from the mean. We're still pretty close."
14.2 says, "Being 4.9 away from the mean is a bit of a stretch, but hey, I like to stand out!"
5.6 says, "I'm 3.7 away from the mean, but who's counting? We all have our quirks."
8.3 says, "Being 0.9 away from the mean means I'm practically a twin! No biggie!"
9.0 says, "I'm only 0.3 away from the mean. We're practically inseparable."
10.2 says, "I'm 0.9 away from the mean, but who's measuring? It's just a small difference."
Now we add up all their emotional distances and divide by 7 (the number of numbers) to get the mean absolute deviation. After some intense calculation, we find that the mean absolute deviation is... 1.7!
So the answer is 1.7, rounding to the nearest tenth. Don't forget to send the numbers some love for sharing their feelings with us!
To find the mean absolute deviation of a dataset, follow these steps:
1. Find the mean of the dataset by adding up all the numbers and dividing by the total count.
mean = (8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7 = 65.1 / 7 = 9.3
2. Find the absolute deviation for each number by subtracting the mean from each number and taking the absolute value.
Absolute deviation for 8.4 = |8.4 - 9.3| = 0.9
Absolute deviation for 9.4 = |9.4 - 9.3| = 0.1
Absolute deviation for 14.2 = |14.2 - 9.3| = 4.9
Absolute deviation for 5.6 = |5.6 - 9.3| = 3.7
Absolute deviation for 8.3 = |8.3 - 9.3| = 1.0
Absolute deviation for 9.0 = |9.0 - 9.3| = 0.3
Absolute deviation for 10.2 = |10.2 - 9.3| = 0.9
3. Find the sum of all the absolute deviations.
Sum of absolute deviations = 0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9 = 11.8
4. Divide the sum of absolute deviations by the total count.
Mean absolute deviation = 11.8 / 7 = 1.685714...
Round the mean absolute deviation to the nearest tenth:
Mean absolute deviation ≈ 1.7
Therefore, the correct response is: 1.7.
To find the mean absolute deviation of a dataset, you need to follow these steps:
1. Calculate the mean (average) of the dataset by adding up all the numbers and dividing by the total count. In this case:
Mean = (8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7 = 65.1 / 7 = 9.3
2. Find the absolute deviation for each number in the dataset. Absolute deviation is the absolute difference between each number and the mean. Subtract the mean from each number and take the absolute value. For example:
Absolute Deviation for 8.4 = |8.4 - 9.3| = 0.9
Absolute Deviation for 9.4 = |9.4 - 9.3| = 0.1
...
Absolute Deviation for 10.2 = |10.2 - 9.3| = 0.9
3. Add up all the absolute deviations calculated in step 2.
Sum of Absolute Deviations = 0.9 + 0.1 + ... + 0.9
4. Divide the sum of the absolute deviations by the total count of numbers in the dataset. In this case:
Mean Absolute Deviation = Sum of Absolute Deviations / Total Count = (0.9 + 0.1 + ... + 0.9) / 7
Calculating the values precisely would require adding up all the absolute deviations and then dividing by 7. However, since you need to round the answer to the nearest tenth, you can approximate the mean absolute deviation by observing the relative magnitudes of the numbers. Looking at the values, it is clear that the absolute deviations are all less than 1.
Therefore, rounding the answer to the nearest tenth:
Mean Absolute Deviation ≈ 1.7
Hence, the correct answer is 1.7.