I have found the mean for each data set, but I am not sure if I have calculated the MAD(mean absolute deviation)for each data set correctly. Can someone please help me?
Calculate the mean of each data set.
Soil A: 61+61+62+65+70+71+75+81+82+90=71.8; =71.8
Soil B: 59+63+69+70+72+73+76+77+78+83=72;
=72
c) Calculate the mean absolute deviation (MAD) of each data set.
Soil A:
│-10.8│²+│-10.8│²+І│9.8│²+│-6.8│²+
│-1.8│²+│-0.8│²+│3.2│²+9.2²+10.2²+18.2²
Soil A: 116.64+116.64+96.04+46.24+3.24+0.64+
10.24+84.64+104.04+331.24=909.60/10 =
√90.96 = (9.5)
Soil B: │-13│²+│-9│²+│-3│²+
│-2│²+0²+1²+4²+5²+6²+11²
Soil B:
169+81+9+4+0+1+16+25+36+121=462/10 = √46.2= 6.8)
To calculate the mean absolute deviation (MAD) for each data set, you are on the right track. However, it seems like you made a mistake in your calculations.
The formula for MAD is the sum of the absolute values of the differences between each data point and the mean, divided by the number of data points. Here's how you can correctly calculate MAD for each data set:
Soil A:
1. Find the mean of Soil A: 71.8 (correctly calculated)
2. Find the absolute deviations for each data point by subtracting the mean from each data point:
|-10.8 - 71.8|, |-10.8 - 71.8|, |9.2 - 71.8|, |-6.8 - 71.8|, |-1.8 - 71.8|,
|-0.8 - 71.8|, |3.2 - 71.8|, |9.2 - 71.8|, |18.2 - 71.8|
3. Square each absolute deviation (optional - MAD can also be calculated without squaring)
4. Sum up all the squared deviations: 116.64 + 116.64 + 96.04 + 46.24 + 3.24 + 0.64 + 10.24 + 84.64 + 104.04 + 331.24 = 909.60
5. Divide the sum of squared deviations by the number of data points (in this case, 10): 909.60 / 10 = 90.96
6. Take the square root of the result to get the MAD: √90.96 ≈ 9.54 (rounded to 2 decimal places)
So the correct MAD for Soil A is approximately 9.54.
Now let's calculate MAD for Soil B:
1. Find the mean of Soil B: 72 (correctly calculated)
2. Find the absolute deviations for each data point by subtracting the mean from each data point:
|-13 - 72|, |-9 - 72|, |-3 - 72|, |-2 - 72|, |0 - 72|,
|1 - 72|, |4 - 72|, |5 - 72|, |6 - 72|, |11 - 72|
3. Square each absolute deviation (optional - MAD can also be calculated without squaring)
4. Sum up all the squared deviations: 169 + 81 + 9 + 4 + 0 + 1 + 16 + 25 + 36 + 121 = 462
5. Divide the sum of squared deviations by the number of data points (in this case, 10): 462 / 10 = 46.2
6. Take the square root of the result to get the MAD: √46.2 ≈ 6.80 (rounded to 2 decimal places)
So the correct MAD for Soil B is approximately 6.80.
Please double-check your calculations to ensure accuracy.