Question

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: 11; IQR: 6.5 MAD: 11; IQR: 6.5 MAD: 11; IQR: 8 MAD: 11; IQR: 8 MAD: 4; IQR: 6.5 MAD: 4; IQR: 6.5 MAD: 4; IQR: 8

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the Mean Absolute Deviation (MAD), first find the median of the data set, which is 11.

Next, find the absolute deviation of each data point from 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

Now, find the average of these absolute deviations:
(10+7+5+4+2+1+1+0+1+1+3+4+6+7+8) / 15 = 60 / 15 = 4

Therefore, the MAD is 4.

To calculate the Interquartile Range (IQR), first find the median of the lower half (Q1) and upper half (Q3) of the data set:
Lower half: 1, 4, 6, 7, 9, 10
Upper half: 11, 12, 12, 14, 15, 17, 18, 19

Q1 = 7 and Q3 = 15

Next, find the IQR:
IQR = Q3 - Q1 = 15 - 7 = 8

Therefore, the IQR is 8.

So, the correct answer is:
MAD: 4; IQR: 8