The coefficient of mean deviation about mean for the first 9 natural n...
Calculating the Mean
To calculate the coefficient of mean deviation about mean for the first 9 natural numbers, we first need to calculate the mean of these numbers.
The formula for calculating the mean is:
Mean = (Sum of all numbers) / (Total number of numbers)
For the first 9 natural numbers, the sum would be:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
And the total number of numbers is 9.
Therefore, the mean would be:
Mean = 45 / 9 = 5
Calculating the Deviations
The next step is to calculate the deviations of each number from the mean.
The formula for calculating deviation is:
Deviation = |(Number - Mean)|
For each of the first 9 natural numbers, the deviations from the mean would be:
|1 - 5| = 4
|2 - 5| = 3
|3 - 5| = 2
|4 - 5| = 1
|5 - 5| = 0
|6 - 5| = 1
|7 - 5| = 2
|8 - 5| = 3
|9 - 5| = 4
Calculating the Mean Deviation
Once we have calculated the deviations, we can calculate the mean deviation by finding the mean of all the deviations.
The formula for calculating mean deviation is:
Mean Deviation = (Sum of all deviations) / (Total number of numbers)
For the first 9 natural numbers, the sum of all deviations would be:
4 + 3 + 2 + 1 + 0 + 1 + 2 + 3 + 4 = 20
And the total number of numbers is 9.
Therefore, the mean deviation would be:
Mean Deviation = 20 / 9 = 2.22 (rounded to two decimal places)
Calculating the Coefficient of Mean Deviation
The final step is to calculate the coefficient of mean deviation, which is simply the mean deviation divided by the mean.
The formula for calculating the coefficient of mean deviation is:
Coefficient of Mean Deviation = (Mean Deviation) / (Mean)
For the first 9 natural numbers, the mean deviation is 2.22 and the mean is 5.
Therefore, the coefficient of mean deviation would be:
Coefficient of Mean Deviation = 2.22 / 5 = 0.44 (rounded to two decimal places)
Conclusion
In conclusion, the coefficient of mean deviation about mean for the first 9 natural numbers is 0.44.