What is the MAD and IQR for the given dataset?
1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19
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.