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: 8 MAD: 11; IQR: 8 MAD: 11; IQR: 6.5 MAD: 11; IQR: 6.5 MAD: 4; IQR: 8 MAD: 4; IQR: 8 MAD: 4; IQR: 6.5
not in my list of answers your wrong
Apologies for the oversight. Let's recalculate.
To calculate the MAD, we first need to find the median of the dataset:
1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19
The median is (10th + 11th) / 2 = (12 + 14) / 2 = 13
Now, we calculate the absolute deviation of each data point from the median:
|1-13|, |4-13|, |6-13|, |7-13|, |9-13|, |10-13|, |10-13|, |11-13|, |12-13|, |12-13|, |14-13|, |15-13|, |17-13|, |18-13|, |19-13|
These calculate to:
12, 9, 7, 6, 4, 3, 3, 2, 1, 1, 1, 2, 4, 5, 6
The MAD is the median of these deviations, so the MAD is 3.
To find the IQR, we first find Q1 and Q3:
Q1 = median of the lower half = median of (1, 4, 6, 7, 9) = 6
Q3 = median of the upper half = median of (12, 12, 14, 15, 17) = 14
IQR = Q3 - Q1 = 14 - 6 = 8
Therefore, the correct answer is:
MAD: 3; IQR: 8
To calculate the Mean Absolute Deviation (MAD) and Interquartile Range (IQR) for the given dataset:
1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19
First, we find the median which is 11.
Then, we calculate the MAD by finding the absolute difference between each data point and the median, then finding the mean of these absolute differences:
(10-11) + (7-11) + (12-11) + (6-11) + (9-11) + (4-11) + (10-11) + (14-11) + (15-11) + (18-11) + (12-11) + (1-11) + (17-11) + (19-11) = 38
MAD = 38 / 15 = 2.53
Next, we find the Q1 and Q3 to calculate the IQR:
Q1 = median of the first half = 9
Q3 = median of the second half = 15
IQR = Q3 - Q1 = 15 - 9 = 6
Therefore, the correct answer is:
MAD: 2.53; IQR: 6.5