find the mean absolute deviation given the dot plot below.
find the mean absolute deviation given the dot plot below.
Answer
Explanation:
Step1: Calculate the mean
The data set is {13, 14, 14, 17, 17, 17, 17, 18}. The sum of the data is (13 + 14\times2+17\times4 + 18=13+28 + 68+18=127). There are (1 + 2+4 + 1=8) data - points. The mean (\bar{x}=\frac{127}{8}=15.875).
Step2: Calculate the absolute deviations
For (x_1 = 13), (|x_1-\bar{x}|=|13 - 15.875| = 2.875). For (x_2 = 14), (|x_2-\bar{x}|=|14 - 15.875| = 1.875) (and there are 2 of them). For (x_3 = 17), (|x_3-\bar{x}|=|17 - 15.875| = 1.125) (and there are 4 of them). For (x_4 = 18), (|x_4-\bar{x}|=|18 - 15.875| = 2.125).
Step3: Calculate the sum of absolute deviations
The sum of absolute deviations is (2.875+1.875\times2 + 1.125\times4+2.125=2.875 + 3.75+4.5+2.125 = 13.25).
Step4: Calculate the mean absolute deviation
The mean absolute deviation (MAD) is (\frac{13.25}{8}=1.65625).
Answer:
(1.65625)