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Bot GPT 3.5 To determine which measure of variability (MAD or IQR) best describes the spread of the data set, we need to calculate both measures and then determine if the data distribution has outliers or if it is skewed.
First, let's calculate the MAD (Mean Absolute Deviation):
1. Find the mean of the data set:
Mean = (0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 3 + 5) / 10
Mean = 1.8
2. Calculate the absolute deviations from the mean for each data point:
|0-1.8|, |0-1.8|, |1-1.8|, |1-1.8|, |1-1.8|, |2-1.8|, |2-1.8|, |3-1.8|, |3-1.8|, |5-1.8|
1.8, 1.8, 0.8, 0.8, 0.8, 0.2, 0.2, 1.2, 1.2, 3.2
3. Find the mean of these absolute deviations:
MAD = (1.8 + 1.8 + 0.8 + 0.8 + 0.8 + 0.2 + 0.2 + 1.2 + 1.2 + 3.2) / 10
MAD = 1.2
Now, let's calculate the IQR (Interquartile Range):
1. First, order the data set: 0, 0, 1, 1, 1, 2, 2, 3, 3, 5
2. Find the median of the data set, which is the value in the middle: 1.5
3. Divide the data set into two halves. Since there are an even number of data points, the lower half is 0, 0, 1, 1 and the upper half is 2, 2, 3, 3, 5.
4. Find the median of each half: Lower median = (0 + 1) / 2 = 0.5, Upper median = (2 + 3) / 2 = 2.5
5. Calculate the IQR: IQR = Upper median - Lower median = 2.5 - 0.5 = 2
Since the MAD is 1.2 and the IQR is 2, the IQR best describes the spread of the data set. Additionally, the data distribution is symmetrical since there are no outliers. Therefore, the correct answer is:
C. IQR; the data distribution is symmetrical