Final answer:
The Mean Absolute Deviation (MAD) of the dataset 20,21,14,29,26,14,23 with a mean of 21 is approximately 4.29, calculated by finding the average of the absolute differences between each data point and the mean.
Step-by-step explanation:
The student has asked to find the Mean Absolute Deviation (MAD) of a given dataset: 20,21,14,29,26,14,23, with a provided mean of 21. To calculate the MAD, we start by finding the absolute differences between each data value and the mean. Then, we calculate the average of these absolute differences to get the MAD.
Steps to calculate MAD:
1. Subtract the mean from each data point and find the absolute value of each difference.
2. Add up all of the absolute differences.
3. Divide the sum of the absolute differences by the number of data points.
Here are the calculations:
• Absolute differences: |20-21|=1, |21-21|=0, |14-21|=7, |29-21|=8, |26-21|=5, |14-21|=7, |23-21|=2
• Sum of absolute differences: 1+0+7+8+5+7+2 = 30
• MAD: 30 / 7 = 4.29 (approximately)
The MAD of the given data set is approximately 4.29.