Find the mean absolute deviation of 8.4 ,9.4 ,14.2 ,5.6 ,8.3 ,9.0 ,10.2 round to the nearest ten
To find the mean absolute deviation, we first calculate the mean of the given numbers. The mean is the sum of all the numbers divided by the total number of values.
Mean = (8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7
Mean = 65.1 / 7
Mean ≈ 9.3
Next, we find the absolute deviation of each number from the mean. The absolute deviation is the absolute value of the difference between each number and the mean.
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
Now, we calculate the mean of these absolute deviations.
Mean of Absolute Deviations = (0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9) / 7
Mean of Absolute Deviations = 11.8 / 7
Mean of Absolute Deviations ≈ 1.7
Rounded to the nearest ten, the mean absolute deviation is 2.
To find the mean absolute deviation, follow these steps:
Step 1: Find the mean (average) of the given numbers.
8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2 = 65.1
Step 2: Subtract the mean from each number to find the deviation.
|8.4 - 65.1| = 56.7
|9.4 - 65.1| = 55.7
|14.2 - 65.1| = 50.9
|5.6 - 65.1| = 59.5
|8.3 - 65.1| = 56.8
|9.0 - 65.1| = 56.1
|10.2 - 65.1| = 54.9
Step 3: Add up all the deviations.
56.7 + 55.7 + 50.9 + 59.5 + 56.8 + 56.1 + 54.9 = 390.6
Step 4: Divide the sum of deviations by the total number of values.
390.6 ÷ 7 = 55.8
Step 5: Round the mean absolute deviation to the nearest ten.
The mean absolute deviation is approximately 60.