VARIANCE AND STANDARD DEVIATION

• Range


  Highest value - Lowest value
• Finding range for group data

  1. Get the highest class boundary

  2. Get the lowest class boundary

  3. Subtract the lowest from the highest
• Variance


  Measure of the spread of a dataset
• Computing variance for group data

  1. Get the total frequency (n)

  2. Get the class marks

  3. Calculate f*x (frequency * class mark)

  4. Get the mean (sum of f*x / n)

  5. Calculate (class mark - mean)^2

  6. Multiply each (class mark - mean)^2 by the frequency

  7. Sum the f*(class mark - mean)^2

  8. Divide the sum by (n-1) to get the variance
• Standard deviation


  Square root of the variance
• Computing standard deviation for group data

  1. Calculate the variance

  2. Take the square root of the variance to get the standard deviation
• The steps to find range, variance and standard deviation for group data are different from individual data
• Measure of variability or dispersion


  A number that conveys the idea of spread for the data set
• Measure of central tendency

  Types of average: mean, median, mode
• Range


  Measures the distance between the largest and the smallest value, gives an idea of the spread of the data set
• Range is affected by outliers and does not consider all values in the data set, so it is not a very useful measure of variability
• Finding the range

  Get the highest value and subtract the lowest value
• Calculating range


  • Machine 1: Highest value 10.07, lowest value 5.85, range = 10.07 - 5.85 = 4.22 ohms
  • Machine 2: Highest value 8.03, lowest value 7.95, range = 8.03 - 7.95 = 0.08 ohms
• Variance

  The square of the standard deviation of the data
• Computing variance of a population


  Σ(x - μ)^2 / n
• Standard deviation


  A measure of how spread out numbers are, the square root of the variance
• Computing standard deviation


  Determine the mean

  2. Calculate the deviation of each number from the mean

  3. Square each deviation and find the sum

  4. Divide the sum by n (population) or n-1 (sample)

  5. Take the square root
• The dependable company produced the most consistent batteries with regards to life expectancy under constant use, as they had the smallest standard deviation