nana measures the lengths of mice. their lengths, in centimeters, are recorded. there are 10 values. 7 12…
nana measures the lengths of mice. their lengths, in centimeters, are recorded. there are 10 values. 7 12 8.5 11 6.5 9 12 7 10 6 what is the mean absolute deviation of the data set? enter the value to the nearest tenth. centimeters
Answer
Explanation:
Step1: Calculate the mean
The data set is (7, 12, 8.5, 12, 7, 11, 6.5, 9, 10, 6). The sum of the data values is (7 + 12+8.5 + 12+7+11+6.5+9+10+6=89). The mean (\bar{x}=\frac{89}{10} = 8.9).
Step2: Calculate the absolute - deviations
For (7): (|7 - 8.9|=1.9); for (12): (|12 - 8.9| = 3.1); for (8.5): (|8.5 - 8.9|=0.4); for (12): (|12 - 8.9| = 3.1); for (7): (|7 - 8.9|=1.9); for (11): (|11 - 8.9| = 2.1); for (6.5): (|6.5 - 8.9|=2.4); for (9): (|9 - 8.9|=0.1); for (10): (|10 - 8.9| = 1.1); for (6): (|6 - 8.9|=2.9).
Step3: Calculate the mean of the absolute - deviations
The sum of the absolute - deviations is (1.9+3.1 + 0.4+3.1+1.9+2.1+2.4+0.1+1.1+2.9 = 18.9). The mean absolute deviation (MAD=\frac{18.9}{10}=1.89\approx1.9).
Answer:
(1.9)