To find the MAD (mean absolute deviation) and IQR (interquartile range) for this dataset, we first need to find the median, quartiles, and calculate the necessary values.
Dataset:
1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19
Sorted Dataset:
1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19
Median (Q2) = 12 (the middle value when the data is in ascending order)
Quartiles:
Q1 (25th percentile) = 9 (the middle value of the 1st half of the dataset)
Q3 (75th percentile) = 15 (the middle value of the 2nd half of the dataset)
IQR (Interquartile Range) = Q3 - Q1 = 15 - 9 = 6
To find the MAD, we need to find the absolute deviations from the median and then calculate the mean of those absolute deviations.
Absolute deviations from the median:
|1-12|, |4-12|, |6-12|, |7-12|, |9-12|, |10-12|, |10-12|, |11-12|, |12-12|, |12-12|, |14-12|, |15-12|, |17-12|, |18-12|, |19-12|
|11|, |8|, |6|, |5|, |3|, |2|, |2|, |1|, |0|, |0|, |2|, |3|, |5|, |6|, |7|
MAD (Mean Absolute Deviation) = Mean of these absolute deviations = (11+8+6+5+3+2+2+1+0+0+2+3+5+6+7) / 15 = 4.4
Therefore, the IQR for the given dataset is 6 and the MAD is 4.4.