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

Answer 1

To find the MAD (mean absolute deviation) and IQR (interquartile range) for the given dataset, first arrange the numbers in ascending order:

1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19

Next, calculate the mean of the dataset:
(1 + 4 + 6 + 7 + 9 + 10 + 10 + 11 + 12 + 12 + 14 + 15 + 17 + 18 + 19) / 15 = 10.4

Calculate the absolute deviations from the mean for each data point:
|1 - 10.4| = 9.4
|4 - 10.4| = 6.4
|6 - 10.4| = 4.4
|7 - 10.4| = 3.4
|9 - 10.4| = 1.4
|10 - 10.4| = 0.4
|10 - 10.4| = 0.4
|11 - 10.4| = 0.6
|12 - 10.4| = 1.6
|12 - 10.4| = 1.6
|14 - 10.4| = 3.6
|15 - 10.4| = 4.6
|17 - 10.4| = 6.6
|18 - 10.4| = 7.6
|19 - 10.4| = 8.6

Calculate the MAD by finding the mean of these absolute deviations:
(MAD) = (9.4 + 6.4 + 4.4 + 3.4 + 1.4 + 0.4 + 0.4 + 0.6 + 1.6 + 1.6 + 3.6 + 4.6 + 6.6 + 7.6 + 8.6) / 15 = 4.56

The MAD for the dataset is 4.56.

To find the IQR, first find the median of the dataset, which is the middle number:
Median = 10

Next, divide the dataset into two halves:
Lower half: 1, 4, 6, 7, 9
Upper half: 12, 12, 14, 15, 17, 18, 19

Find the median of each half:
Lower median = 6
Upper median = 15

Calculate the IQR by finding the difference between the upper and lower median:
IQR = Upper median - Lower median
IQR = 15 - 6
IQR = 9

The IQR for the dataset is 9.