standard deviation

• What does standard deviation measure?

  The spread of data about the mean
• Why is standard deviation useful in comparing data?

  It compares sets with the same mean but different ranges
• What is the formula for standard deviation?

  $S = \sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}$
• What does $x$ represent in the standard deviation formula?

  Value in the data set
• What does $\bar{x}$ represent in the standard deviation formula?

  Mean of the values in the data set
• What does $n$ represent in the standard deviation formula?

  Number of values in the data set
• Do you need to memorize the standard deviation formula?

  No, it's on the N5 Apps formula sheet
• What is the easier method to calculate standard deviation mentioned?

  The table method
• How do you calculate the mean of the given birth weights?

  • Add all weights: $2.5 + 4.5 + 3.7 + 2.1 + 3.8 + 3.4 = 21$
  • Divide by the number of weights: $\bar{x} = \frac{21}{6} = 3.5$
• What is the mean of the birth weights given?

  1. 5 kg
• How do you calculate the standard deviation for the birth weights?

  1. Calculate deviations: $(x - \bar{x})$
  2. Square deviations: $(x - \bar{x})^2$
  3. Sum squared deviations: $\sum = 2.3$
  4. Apply formula: $S = \sqrt{\frac{2.3}{5}} \approx 0.68$
• What is the standard deviation of the birth weights?

  Approximately 0.68 kg
• What is the total of the squared deviations for the birth weights?

  1. 3
• How many weights were recorded in the example?

  6 weights