Find the MAD of the data set: 2,4,5,6,8,9,13,14,15,18. Round to the nearest hundredth as needed.
To find the MAD (mean absolute deviation) of the given data set:
1. Find the mean: add all the numbers and divide by the total count:
mean = (2+4+5+6+8+9+13+14+15+18)/10 = 10
2. Find the absolute deviation of each data point from the mean: subtract the mean from each number and take the absolute value:
|2-10|=8, |4-10|=6, |5-10|=5, |6-10|=4, |8-10|=2, |9-10|=1, |13-10|=3, |14-10|=4, |15-10|=5, |18-10|=8
3. Find the average of these absolute deviations: add up all the absolute deviations and divide by the total count:
(8+6+5+4+2+1+3+4+5+8)/10 = 4.6
Therefore, the MAD of the given data set is 4.6 (rounded to the nearest hundredth).
To find the Mean Absolute Deviation (MAD) of a data set, follow these steps:
1. Calculate the mean (average) of the data set by adding up all the numbers and dividing the sum by the total number of values:
(2 + 4 + 5 + 6 + 8 + 9 + 13 + 14 + 15 + 18) / 10 = 94 / 10 = 9.4
2. Subtract the mean from each value in the data set to find the deviation of each value from the mean:
2 - 9.4 = -7.4
4 - 9.4 = -5.4
5 - 9.4 = -4.4
6 - 9.4 = -3.4
8 - 9.4 = -1.4
9 - 9.4 = -0.4
13 - 9.4 = 3.6
14 - 9.4 = 4.6
15 - 9.4 = 5.6
18 - 9.4 = 8.6
3. Take the absolute value of each deviation to remove the negative sign:
|-7.4| = 7.4
|-5.4| = 5.4
|-4.4| = 4.4
|-3.4| = 3.4
|-1.4| = 1.4
|-0.4| = 0.4
|3.6| = 3.6
|4.6| = 4.6
|5.6| = 5.6
|8.6| = 8.6
4. Find the average of these absolute deviations by adding them up and dividing by the total number of values (10 in this case):
(7.4 + 5.4 + 4.4 + 3.4 + 1.4 + 0.4 + 3.6 + 4.6 + 5.6 + 8.6) / 10 = 44.8 / 10 = 4.48
5. Round the MAD to the nearest hundredth:
MAD = 4.48 (rounded to the nearest hundredth)
Therefore, the Mean Absolute Deviation (MAD) of the given data set is 4.48 (rounded to the nearest hundredth).