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 (1 point) Responses MAD: 4; IQR: 6.5 MAD: 4; IQR: 6.5 MAD: 11; IQR: 6.5 MAD: 11; IQR: 6.5 MAD: 11; IQR: 8 MAD: 11; IQR: 8 MAD: 4; IQR: 8
To find the MAD (Mean Absolute Deviation) for the given dataset, we first need to find the mean of the dataset which is:
(1+4+6+7+9+10+10+11+12+12+14+15+17+18+19) / 15 = 10.4
Next, we find the absolute deviation of each data point from the mean:
|1-10.4| = 9.4
|4-10.4| = 6.4
|6-10.4| = 4.4
|7-10.4| = 3.4
|9-10.4| = 1.4
|10-10.4| = 0.4
|10-10.4| = 0.4
|11-10.4| = 0.6
|12-10.4| = 1.6
|12-10.4| = 1.6
|14-10.4| = 3.6
|15-10.4| = 4.6
|17-10.4| = 6.6
|18-10.4| = 7.6
|19-10.4| = 8.6
Now, we find the average of these absolute deviations which is the MAD:
(9.4+6.4+4.4+3.4+1.4+0.4+0.4+0.6+1.6+1.6+3.6+4.6+6.6+7.6+8.6) / 15 = 4
So, the MAD for the given dataset is 4.
To find the IQR (Interquartile Range) for the dataset, we first need to find the median which is the value at the middle position of the dataset when it is arranged in ascending order.
Median = 10
Next, we divide the dataset into two halves based on the median. The lower half is {1, 4, 6, 7, 9, 10} and the upper half is {11, 12, 12, 14, 15, 17, 18, 19}. We find the median of each half, which are 7.5 and 14 respectively.
IQR = Upper Quartile (Q3) - Lower Quartile (Q1) = 14 - 7.5 = 6.5
Therefore, the MAD is 4 and the IQR is 6.5 for the given dataset.
Therefore, the correct answer is: MAD: 4; IQR: 6.5.