What is the MAD and IQR for the given dataset?

Question

1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19
(1 point)
O MAD: 11; IQR: 8
○ MAD: 4; IQR: 6.5
○ MAD: 4; IQR: 8
MAD: 11; IQR: 6.5

Answer 1

To calculate the MAD (Mean Absolute Deviation) and IQR (Interquartile Range) for the given dataset:
1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19

First, we need to find the median of the dataset, which is the middle number when the numbers are arranged in ascending order. In this case, the median is 11.

Next, we calculate the MAD:
1. Find the absolute difference 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

2. Calculate the average of these absolute differences:
(10+7+5+4+2+1+1+0+1+1+3+4+6+7+8) / 15 = 59 / 15 = 3.93

So, the MAD is approximately 3.93.

Next, we calculate the IQR:
1. Arrange the data in ascending order:
1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19

2. Find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data and Q3 is the median of the upper half.
Q1 = median of {1, 4, 6, 7, 9} = 6
Q3 = median of {14, 15, 17, 18, 19} = 17

3. Calculate the IQR:
IQR = Q3 - Q1 = 17 - 6 = 11

So, the IQR is 11.

Therefore, the MAD for the dataset is approximately 3.93, and the IQR is 11.