Math week 7

• Measure of variability


  Describes the degree of spread or amount of dispersion among the values in a distribution or data set
• Measures of variability


  • Range
  • Average deviation
  • Variance
  • Standard deviation
• Range

  The difference between the highest score and the lowest score
• Calculating range of ungrouped data

  1. R = HS - LS

  2. Where: R - Range, HS - Highest Score, LS - Lowest Score
• Calculating range

  • Example 1: Range of scores 98, 92, 95, 88, 90, 86, 91, 89, 95, 87 is 98 - 86 = 12
  • Example 2: Range of Group A scores 12, 7, 9, 10, 11 is 12 - 7 = 5, Range of Group B scores 2, 18, 20, 8, 5 is 20 - 2 = 18
• Average deviation


  The dispersion of a set of data about the average of these data
• Calculating average deviation of ungrouped data


  1. AD = Σ|x - x̄| / n

  2. Where: AD - Average Deviation, x - individual score, x̄ - mean, n - number of values/scores
• Calculating average deviation

  • Example 1: Average deviation of scores 9, 12, 15, 16 is 2.5
  • Example 2: Average deviation of scores 98, 95, 80, 73, 64 is 11.6
• Variance


  The quotient of the sum of the squared deviations from the mean divided by n-1
• Standard deviation


  The square root of the variance
• Calculating variance and standard deviation of ungrouped data


  1. Variance (s^2) = Σ(x - x̄)^2 / (n-1)

  2. Standard Deviation (s) = √(Σ(x - x̄)^2 / (n-1))

  3. Where: s^2 - variance, s - standard deviation, x - individual score, x̄ - mean, n - number of values/scores
• Calculating variance and standard deviation


  • Example 1: Variance of scores 1, 3, 7, 9, 15, 19 is 32.67, Standard deviation is 5.72
• Standard deviation cannot be negative
• Standard deviation of a set of data can be equal to zero if and only if the observations are equal values
• Standard deviation should have a value which is equal to approximately one-third of the range
• Computing variance and standard deviation of a set of data


  1. Find the mean

  2. Subtract the mean from each score, get the absolute values of the deviations

  3. Compute the variance using the formula

  4. Compute the standard deviation by taking the square root of the variance
• The standard deviation of a set of data can be equal to zero if and only if the observations are equal values
• The standard deviation should have a value which is equal to approximately one-third of the range
• Range


  The difference between the upper class boundary and the lower class boundary
• Computing the range of grouped data

  1. Find the upper class boundary

  2. Find the lower class boundary

  3. Subtract the lower class boundary from the upper class boundary
• Average deviation


  The dispersion of a set of data about the mean of these data
• Computing the average deviation of grouped data

  1. Find the mean

  2. Subtract the mean from each classmark, get the absolute values

  3. Multiply each frequency by the corresponding absolute deviation

  4. Sum the products and divide by the total frequency
• Variance


  The mean of the square of the deviations from the mean of a frequency distribution
• Standard deviation


  The best indicator of the degree of dispersion among the measures of variability, representing an average variability of the distribution
• Computing the variance and standard deviation of grouped data

  1. Find the mean

  2. Compute the variance using the formula

  3. Compute the standard deviation by taking the square root of the variance
• Column A


  • 8, 10, 7, 12, 27, 30, 18
  • 35, 47, 22, 49, 18, 13, 15
  • 89, 98, 75, 63, 82, 87, 93
  • 73, 81, 78, 92, 89, 90, 74
  • 127, 278, 485, 186, 389
• Column B


  • 36
  • 358
  • 19
  • 23
  • 35
• Activity 1.2 Compute Me

  1. The data shows the number of absences of grade 7 students in a particular school from June to December: 32, 28, 40, 81, 70, 49

  2. The following data are the list of prices of different brands of cellphones in the mall: ₱2 000, ₱3 500, ₱1 500, ₱5 000, ₱3 000
• Activity 1.3 Complete Me

  • Mean
  • Variance
  • Standard Deviation
• n = 20
• Σf𝑋𝑚 =740
• Σf( 𝑥𝑚 − 𝑥 )𝟐 = 1 130
• 𝑥 = 37
• x


  • 6
  • 8
  • 10
  • 12
  • 17
  • 19
• n = 6
• Σ( 𝑥 − 𝑥 )𝟐= _______
• Activity 2.1 Find Me


  1. Range

  2. Range

  3. Range
• Activity 2.2 You Complete Me


  1. Complete the table by filling the missing values

  2. Find the mean and the average deviation
• Activity 2.3 Find Me and Complete Me

  1. Complete the table by filling the missing values

  2. Find the variance and standard deviation
• Range (ungrouped data)


  R = HS - LS