Question

1. science skills. calculations. exercises.

student name: ______
worked example
measurements of pendulum period: 2.0 s, 2.1 s, 1.9 s

1. mean (average): average = \\(\frac{\text{sum of all results}}{\text{number of results}}\\)

average = \\(\frac{\text{sum of all results}}{\text{number of results}} = \frac{2.0 + 2.1 + 1.9}{3} = 2.0\\)s

1. range: range = maximum − minimum

range = maximum − minimum = 2.1 − 1.9 = 0.2s

1. random error: random = \\(\frac{\text{maximum−minimum}}{2}\\)

random = \\(\frac{\text{maximum−minimum}}{2} = \frac{2.1−1.9}{2} = 0.1\\)s

1. result with error: average ± random error

average ± random error = 2.0 ± 0.1s

1. percentage uncertainty: % of uncertainty = \\(\frac{\text{random error}}{\text{average}} \cdot 100\\)

% of uncertainty < 10% good measurement
% of uncertainty > 10% bad measurement
% of uncertainty = \\(\frac{\text{random error}}{\text{average}} \cdot 100 = \frac{0.1}{2.0} \cdot 100 = 5\\%\\)
5% < 10% good measurement

1. outliers: mistakes on the data. disregard values that far apart from the rest.

exercise 1: times for a ball falling: 1.2 s, 1.3...
a) find the average: \\(\frac{1.2 + 1.3 + 1.4}{3}\\)
b) find the range: 1.4 − 1.2 = 0.2...
c) find the random error: \\(\frac{1.4 − 1.2}{2}\\)
d) write the result with the error:
e) percentage of uncertainty:

exercise 2: a block is weighed: 250 g, 251 g, 2...
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:

Exercise 1 (Times for a ball falling: 1.2 s, 1.3 s, 1.4 s – assuming the third value is 1.4 s as per the visible text)

a) Find the average

Step1: Sum the values

Sum = \( 1.2 + 1.3 + 1.4 \) = \( 3.9 \)

Step2: Divide by number of values (3)

Average = \( \frac{3.9}{3} \) = \( 1.3 \) s

Step1: Identify maximum and minimum

Maximum = \( 1.4 \) s, Minimum = \( 1.2 \) s

Step2: Subtract minimum from maximum

Range = \( 1.4 - 1.2 \) = \( 0.2 \) s

Step1: Use formula \( \text{Random Error} = \frac{\text{Maximum} - \text{Minimum}}{2} \)

Random Error = \( \frac{1.4 - 1.2}{2} \) = \( \frac{0.2}{2} \) = \( 0.1 \) s

Answer:

\( 1.3 \) s

b) Find the range