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: 4; IQR: 8 MAD: 4; IQR: 8 MAD: 11; IQR: 6.5 MAD: 11; IQR: 6.5 MAD: 11; IQR: 8 MAD: 11; IQR: 8
To calculate the Mean Absolute Deviation (MAD), we first need to find the median of the dataset. The median is 11. Then we find the absolute deviations from the median for each data point:
|1-11| = 10
|4-11| = 7
|6-11| = 5
|7-11| = 4
|9-11| = 2
|10-11| = 1
|10-11| = 1
|11-11| = 0
|12-11| = 1
|12-11| = 1
|14-11| = 3
|15-11| = 4
|17-11| = 6
|18-11| = 7
|19-11| = 8
Now we calculate the Mean Absolute Deviation:
MAD = (10+7+5+4+2+1+1+0+1+1+3+4+6+7+8) / 15
MAD = 60 / 15
MAD = 4
The Interquartile Range (IQR) is the difference between the 3rd quartile (Q3) and the 1st quartile (Q1). To find the quartiles, we first need to order the data:
1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19
There are 15 data points, so the median is the 8th value: 11
Q1 is the median of the lower half of the data: 6
Q3 is the median of the upper half of the data: 15
IQR = Q3 - Q1
IQR = 15 - 6
IQR = 9
Therefore, the MAD is 4 and the IQR is 9.
Answer: MAD: 4; IQR: 9