Question

exercise 5: measuring length of a metal rod: 49.8 cm, 50.1 cm, 50.0 cm, 95.0 cm
a) find the average:
b) find the range:
c) find the random error:
d) write the result with the error:
e) percentage of uncertainty:

Explanation:

Part a)

Step1: Sum the measurements

Sum = \( 49.8 + 50.1 + 50.0 + 95.0 = 244.9 \) cm

Step2: Divide by number of measurements (4)

Average = \( \frac{244.9}{4} = 61.225 \) cm

Step1: Identify max and min

Max = \( 95.0 \) cm, Min = \( 49.8 \) cm

Step2: Subtract min from max

Range = \( 95.0 - 49.8 = 45.2 \) cm

Step1: Exclude the outlier (95.0 cm, as it's inconsistent)

New measurements: \( 49.8, 50.1, 50.0 \)

Step2: Find range of valid data

Range (valid) = \( 50.1 - 49.8 = 0.3 \) cm

Step3: Random error = range / 2

Random error = \( \frac{0.3}{2} = 0.15 \) cm

Answer:

\( 61.225 \) cm

Part b)