The numbers below represent the speeds of the last 6 vehicles that a police officer recorded:
68, 72, 78, 59, 73, 70
Find the mean absolute deviation of the numbers, and round to the nearest tenth if necessary.
To find the mean absolute deviation, we first need to find the mean of the speeds:
Mean = (68 + 72 + 78 + 59 + 73 + 70) / 6
Mean = 420 / 6
Mean = 70
Next, we find the absolute differences between each speed and the mean:
|68-70| = 2
|72-70| = 2
|78-70| = 8
|59-70| = 11
|73-70| = 3
|70-70| = 0
Then, we calculate the sum of the absolute differences:
2 + 2 + 8 + 11 + 3 + 0 = 26
Finally, we divide this sum by the total number of speeds (6) to find the mean absolute deviation:
Mean absolute deviation = 26 / 6
Mean absolute deviation = 4.33
So, the mean absolute deviation of the speeds is approximately 4.3 (rounded to the nearest tenth).