To calculate the mean absolute deviation (MAD), first calculate the mean of the data set:
(1 + 4 + 6 + 7 + 9 + 10 + 10 + 11 + 12 + 12 + 14 + 15 + 17 + 18 + 19) / 15 = 10.6
Next, calculate the absolute deviations for each data point from the mean:
|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
Calculate the sum of the absolute deviations:
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 = 60.4
Calculate the MAD:
MAD = 60.4 / 15 = 4.03
To calculate the interquartile range (IQR), first arrange the data set in ascending order:
1, 4, 6, 7, 9, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19
Calculate the first quartile (Q1) and the third quartile (Q3) using the formula:
Q1 = (n+1)/4 th term
Q3 = 3(n+1)/4 th term
In this case, n = 15:
Q1 = 4th term = 7
Q3 = 11th term = 14
Calculate the IQR:
IQR = Q3 - Q1 = 14 - 7 = 7
Therefore, the MAD is 4.03 and the IQR is 7 for the given data set.
What is the MAD And IR for the given date set
One, four, six, seven, nine, 10, 10, 11, 12, 12, 14, 15, 17, 18, 19,
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