Lesson 2 - Standard Deviation and Errors

• What is the absolute error formula?

  Absolute error = true value - indicated value
• How is absolute error calculated in an experiment?

  By subtracting the indicated value from the true value
• If the indicated value is $990 \text{ m/s}^2$ and the true value is $981 \text{ m/s}^2$, what is the absolute error?


  $0.09 \text{ m/s}^2$
• What is relative error?

  Relative error = (absolute error / true value) x 100%
• How is relative error expressed?

  As a percentage of the true value
• If the density of pure water is $1000 \text{ kg/m}^3$ and measured density is $1000 \text{ kg/m}^3$, what is the relative error?


  $0.25\%$
• What does a precise set of results indicate?

  Results are close to each other
• What does an accurate set of results indicate?

  Results are close to the true value
• How do precision and accuracy differ in measurements?

  • Precision: Results close to each other
  • Accuracy: Results close to the true value
• What is the formula for standard deviation?

  $S =$$\sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i - \bar{x})^2}$
• What does standard deviation measure?

  It measures the precision of data
• If a sample has a mean of $50$ and a range of $80$, what does this indicate about its precision?


  It indicates low precision
• What is the formula for the sample mean?

  <latex}\bar{x} = \frac{\sum x_i}{n}</latex>
• What does a larger standard deviation indicate?

  It indicates lower precision
• If the standard deviation is $19.5$ and the number of data points is $20$, what is the standard error?


  $4.38$
• What is the density of gold?

  19.3 g/cm³
• If the experimentally determined density of gold is $15.1 \text{ g/cm}^3$, what is the absolute error?


  $4.2 \text{ g/cm}^3$
• If the acceleration of gravity is $9.81 \text{ m/s}^2$ and measured to be $9.93 \text{ m/s}^2$, what is the absolute error?


  $0.12 \text{ m/s}^2$
• What is the smallest measurement on the main scale of a Vernier caliper?

  0.1 cm or 1 mm
• How can the width be read using Vernier calipers?

  To the nearest 0.05 cm or 0.5 mm
• If the main scale reading is $11 \text{ cm}$ and the Vernier scale reading is $0.65 \text{ mm}$, what is the total measurement?


  $11.65 \text{ mm}$
• What is the main scale reading of a micrometer?

  0-25 mm
• How is the total measurement of a micrometer calculated?

  By adding the main line reading and thimble scale measurement
• If the index line reading is $7 \text{ mm}$ and the thimble scale reading is $0.14 \text{ mm}$, what is the total measurement?


  $7.14 \text{ mm}$
• If the index line reading is $5.5 \text{ mm}$ and the thimble scale reading is $0.28 \text{ mm}$, what is the total measurement?


  $5.78 \text{ mm}$
• What are the key differences between standard deviation and standard error?

  • Standard deviation: variability within a sample
  • Standard error: variability across samples
• What are the steps to measure using a Vernier caliper?

  1. Read the main scale.
  2. Read the Vernier scale.
  3. Add both measurements for total.
• What are the steps to measure using a micrometer?

  1. Read the main line.
  2. Read the thimble scale.
  3. Add both measurements for total.