B MAD: 4; IQR: 6.5
To calculate the Mean Absolute Deviation (MAD), we first find the mean of the dataset which is:
(1+4+6+7+9+10+10+11+12+12+14+15+17+18+19)/15 = 10.8
Then, we find the absolute deviations from the mean for each data point:
|1-10.8| = 9.8
|4-10.8| = 6.8
|6-10.8| = 4.8
|7-10.8| = 3.8
|9-10.8| = 1.8
|10-10.8| = 0.8
|10-10.8| = 0.8
|11-10.8| = 0.2
|12-10.8| = 1.2
|12-10.8| = 1.2
|14-10.8| = 3.2
|15-10.8| = 4.2
|17-10.8| = 6.2
|18-10.8| = 7.2
|19-10.8| = 8.2
The sum of these absolute deviations is 61.2, and dividing by 15 gives MAD = 4.08
To calculate the Interquartile Range (IQR), we first find the median, which is the middle value when the data points are arranged in ascending order.
The median is the average of the two middle values, which are 10 and 12. So, the median is 11.
Next, we find the first quartile (Q1) which is the median of the data points to the left of the overall median.
The data points to the left of the overall median are: 1, 4, 6, 7, 9, 10, 10
The median of these values is the average of 6 and 7, which is 6.5.
Similarly, we find the third quartile (Q3) which is the median of the data points to the right of the overall median.
The data points to the right of the overall median are: 12, 12, 14, 15, 17, 18, 19
The median of these values is the average of 14 and 15, which is 14.5.
Finally, IQR = Q3 - Q1 = 14.5 - 6.5 = 8
So, the correct answer is B MAD: 4; IQR: 6.5
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)
A MAD: 11; IQR: 8
B MAD: 4; IQR: 6.5
C MAD: 4; IQR: 8
D MAD: 11; IQR: 6.5
1 answer