A dataset includes the point 34.6. The mean of the set is 32.1. What is the absolute deviation for this data point? Round the answer to the nearest tenth.(1 point)
The absolute deviation for the data point 34.6 is 2.5.
Explanation:
Absolute deviation is the absolute value of the difference between a data point and the mean of the entire dataset.
|34.6 - 32.1| = 2.5
Rounding to one decimal place, the answer is 2.5.
Sarina tracks her time spent on homework each night for a week, in minutes. She collects the following times: 51, 60, 25, 15, 20, 5, 35. When she solves for the mean absolute deviation, what number will she use for the divisor?(1 point)
Sarina will use the total number of observations, which is 7, as the divisor when finding the mean absolute deviation.
Explanation:
To find the mean absolute deviation, you first find the absolute deviation of each data point by subtracting the mean from the value, then take the mean of those absolute deviations. The formula is:
Mean absolute deviation = 1/n * (|x1 - mean| + |x2 - mean| + ... + |xn - mean|)
In this case, there are 7 data points, so the divisor will be 7.
What is the sum of the absolute deviations in the following dataset: 68, 51, 75, 78, 94, 35? The mean is 66.8.(1 point)
To find the sum of the absolute deviations in the given dataset:
Step 1: Find the absolute deviation of each data point by subtracting the mean from the value, and taking the absolute value.
|68 - 66.8| = 1.2
|51 - 66.8| = 15.8
|75 - 66.8| = 8.2
|78 - 66.8| = 11.2
|94 - 66.8| = 27.2
|35 - 66.8| = 31.8
Step 2: Add up the absolute deviations.
1.2 + 15.8 + 8.2 + 11.2 + 27.2 + 31.8 = 95.2
Therefore, the sum of the absolute deviations in the given dataset is 95.2.
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
Step 1: Find the mean of the dataset.
8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2 = 65.1
65.1 / 7 = 9.3
So the mean of the dataset is 9.3.
Step 2: Find the absolute deviation of each data point by subtracting the mean from the value, and taking the absolute value.
|8.4 - 9.3| = 0.9
|9.4 - 9.3| = 0.1
|14.2 - 9.3| = 4.9
|5.6 - 9.3| = 3.7
|8.3 - 9.3| = 1.0
|9.0 - 9.3| = 0.3
|10.2 - 9.3| = 0.9
Step 3: Find the mean of those absolute deviations.
(0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9) / 7 = 1.6
Therefore, the mean absolute deviation of the given dataset is 1.6 (rounded to the nearest tenth).