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: 8 MAD: 11; IQR: 8 MAD: 11; IQR: 6.5 MAD: 11; IQR: 6.5 MAD: 4; IQR: 8
To calculate the Mean Absolute Deviation (MAD), first find the median of the dataset, which is 11. Then, calculate the absolute differences between each data point and the median:
|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
Add up all the absolute differences and divide by the total number of data points (15) to get the MAD:
(10+7+5+4+2+1+1+0+1+1+3+4+6+7+8) / 15 = 60 / 15 = 4
Therefore, the MAD for the dataset is 4.
To calculate the Interquartile Range (IQR), first find the first quartile (Q1) and third quartile (Q3) of the dataset. Q1 is the median of the lower half of the dataset which is 7, while Q3 is the median of the upper half of the dataset which is 15.
Then, subtract Q1 from Q3 to get the IQR:
15 - 7 = 8
Therefore, the IQR for the dataset is 8.
Thus, the correct answer is: MAD: 4; IQR: 8.
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The answer is: MAD: 4, IQR: 8