Please tell me if this is correct...Finding the mean, the average deviation from the mean, the standard deviation from the mean, and the relative deviation from the mean...of 10.1, 10.4 and 10.6
Mean-10.4
Average deviation-0.167
Standard deviation-0.25
Relative deviation-2%
Those look ok to me but I wonder why you rounded to 2% instead of 2.4% for RSD. You're allowed two places aren't you?
Yes, that does look better :)
To verify if the provided values for the mean, average deviation, standard deviation, and relative deviation are correct, we need to calculate them step by step using the given data.
1. Finding the mean:
The mean is the sum of all values divided by the total number of values. In this case, the given values are 10.1, 10.4, and 10.6:
Mean = (10.1 + 10.4 + 10.6) / 3
Mean = 31.1 / 3
Mean ≈ 10.3667
Thus, the correct mean for the given values should be 10.3667, not 10.4 as stated.
2. Finding the average deviation from the mean:
The average deviation is calculated by finding the absolute difference between each value and the mean, summing them up, and dividing by the total number of values:
Average deviation = (|10.1 - mean| + |10.4 - mean| + |10.6 - mean|) / 3
Average deviation = (|10.1 - 10.3667| + |10.4 - 10.3667| + |10.6 - 10.3667|) / 3
Average deviation ≈ (0.2667 + 0.0333 + 0.2333) / 3
Average deviation ≈ 0.5333 / 3
Average deviation ≈ 0.1778
Therefore, the correct average deviation from the mean for the given values is approximately 0.1778, not 0.167 as stated.
3. Finding the standard deviation from the mean:
The standard deviation is a measure of the dispersion of the data points from the mean. It is calculated by taking the square root of the sum of the squared differences between each value and the mean, divided by the total number of values:
Standard deviation = √[( (10.1 - mean)^2 + (10.4 - mean)^2 + (10.6 - mean)^2 ) / 3]
Standard deviation ≈ √[( (10.1 - 10.3667)^2 + (10.4 - 10.3667)^2 + (10.6 - 10.3667)^2 ) / 3]
Standard deviation ≈ √[(0.0711 + 0.0009 + 0.0533) / 3]
Standard deviation ≈ √[0.0417 / 3]
Standard deviation ≈ √0.0139
Standard deviation ≈ 0.1179
Hence, the correct standard deviation from the mean for the given values should be approximately 0.1179, not 0.25 as stated.
4. Finding the relative deviation from the mean:
The relative deviation is calculated by dividing the average deviation from the mean by the mean, and then multiplying by 100% to express it as a percentage:
Relative deviation = (average deviation / mean) * 100%
Relative deviation ≈ (0.1778 / 10.3667) * 100%
Relative deviation ≈ 0.0171 * 100%
Relative deviation ≈ 1.71%
Consequently, the correct relative deviation from the mean for the given values is approximately 1.71%, not 2% as stated.
To summarize, the correct calculations for the given values are as follows:
- Mean: 10.3667
- Average deviation from the mean: 0.1778
- Standard deviation from the mean: 0.1179
- Relative deviation from the mean: 1.71%