Find the mean deviation of the distribution 12,6,7,3,15,10,18,5
To find the mean deviation of a distribution, follow these steps:
Step 1: Find the mean (average) of the distribution.
Step 2: Find the deviation of each data point from the mean.
Step 3: Take the absolute value of each deviation.
Step 4: Find the mean of the absolute deviations.
Let's calculate the mean deviation of the given distribution:
Step 1: Find the mean (average):
To find the mean, add up all the values and divide by the total number of values.
Mean = (12 + 6 + 7 + 3 + 15 + 10 + 18 + 5) / 8
Mean = 76 / 8
Mean = 9.5
Step 2: Find the deviation of each data point from the mean:
Subtract the mean from each data point to find the deviation.
Deviation of 12 = 12 - 9.5 = 2.5
Deviation of 6 = 6 - 9.5 = -3.5
Deviation of 7 = 7 - 9.5 = -2.5
Deviation of 3 = 3 - 9.5 = -6.5
Deviation of 15 = 15 - 9.5 = 5.5
Deviation of 10 = 10 - 9.5 = 0.5
Deviation of 18 = 18 - 9.5 = 8.5
Deviation of 5 = 5 - 9.5 = -4.5
Step 3: Take the absolute value of each deviation:
Since mean deviation requires the absolute value of each deviation, remove the negative signs (if any).
Absolute deviation of 2.5 = 2.5
Absolute deviation of -3.5 = 3.5
Absolute deviation of -2.5 = 2.5
Absolute deviation of -6.5 = 6.5
Absolute deviation of 5.5 = 5.5
Absolute deviation of 0.5 = 0.5
Absolute deviation of 8.5 = 8.5
Absolute deviation of -4.5 = 4.5
Step 4: Find the mean of the absolute deviations:
Find the average of all the absolute deviations.
Mean Deviation = (2.5 + 3.5 + 2.5 + 6.5 + 5.5 + 0.5 + 8.5 + 4.5) / 8
Mean Deviation = 34.5 / 8
Mean Deviation = 4.3125
Therefore, the mean deviation of the given distribution is approximately 4.3125.