Students launch a ball ten times and find the results for the range in centimete
ID: 2135785 • Letter: S
Question
Students launch a ball ten times and find the results for the range in centimeters to be 133.3, 127.2, 130.6, 130.5, 128.7, 128.5, 132.9, 131.0, 130.7, and 135.0.
iv) What is the uncertainty in any single range measurement? [Hint: Think "standard deviation of measured values".] (I know it's 2.383 cm)
v) What is the standard error of the mean in the average range in cm?
vi) Suppose the launch angle were the same for all ten trials, but only known (measured) to 1.2% . You would then expect the angular uncertainty to increase the spread in the measured range values by what %?
Explanation / Answer
a. Average range = (133.3+ 127.2+ 130.6+ 130.5+ 128.7+ 128.+ 132.9+ 131.0+130.7+ 135.0)/10
b. standard deviation = sqrt{{sigma(X-M)^2}/n}}
just substitute the values u ll get the answer as 2.38337
c. standard error = 2.38337/sqrt(10) = 0.753