Question

Six students measure the acceleration (in meters per second per second) of an object in free fall. The measured values are: 10.56, 9.52, 9.73, 9.80, 9.78, 10.91.The students want to state that the absolute deviation of each measured value xfrom the mean is at most

d. Find the value of
d.

Answer 1

The measured data is
x = [10.56, 9.52, 9.73, 9.80, 9.78, 10.91]

There are 6 measurements.
Calculate the mean.
m = (10.56+9.52+9.73+9.80+9.78+10.91)/6 = 10.05

Calculate deviations from the mean.
y = |x - m|
= [0.51, 0.53, 0.32, 0.25, 0.27, 0.86]

The greatest deviation from the mean is d = 0.86.

Calculate the average absolute deviation.
(0.51+0.53+0.32+0.25+0.27+0.86)/6 = 0.4567

Answer:
d = 0.86