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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the Mean Absolute Deviation (MAD), first find the mean of the dataset:

Mean = (1+4+6+7+9+10+10+11+12+12+14+15+17+18+19) / 15 = 10.6

Next, calculate the absolute deviation for each data point:

|1-10.6| = 9.6
|4-10.6| = 6.6
|6-10.6| = 4.6
|7-10.6| = 3.6
|9-10.6| = 1.6
|10-10.6| = 0.6
|10-10.6| = 0.6
|11-10.6| = 0.4
|12-10.6| = 1.4
|12-10.6| = 1.4
|14-10.6| = 3.4
|15-10.6| = 4.4
|17-10.6| = 6.4
|18-10.6| = 7.4
|19-10.6| = 8.4

Now, find the mean of the absolute deviations:

MAD = (9.6+6.6+4.6+3.6+1.6+0.6+0.6+0.4+1.4+1.4+3.4+4.4+6.4+7.4+8.4) / 15 = 59.4 / 15 = 3.96

Therefore, the MAD is 3.96.

To calculate the Interquartile Range (IQR), first find the 25th and 75th percentiles:

Q1 = 6.5
Q3 = 14.5

IQR = Q3 - Q1 = 14.5 - 6.5 = 8

Therefore, the IQR is 8.

Thus, the correct answer is: MAD: 3.96; IQR: 8.