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• Measures of position


  Shows where a certain data point or value falls in a sample or array of distribution
• Quartiles


  Points that divide the data into four equal parts
• Q1


  A number such that at most one-fourth or 25% of the data are smaller in value than Q1 and at most three-fourths or 75% are larger than Q1. It is also called lower quartile.
• Q2


  A number such that at most one-half or 50% of the data are below and above in value than Q2. Second Quartile is also known as median.
• Q3


  A number such that at most three-fourths or 75% of the data are smaller in value than Q3 and at most one-fourth or 25% are larger than Q3. It is also called the upper quartile.
• Deciles


  The nine score points that divide the data into ten equal parts
• D3


  A number such that at most 30% of the data are smaller in value than D3 and at most 70% are larger than D3
• D5


  A number such that at most one-half or 50% of the data are below and above in value than D5. It is the median of the set of data. It is also the Q2.
• D9


  A number such that at most 90% of the data are smaller in value than D9, and at most 10% are larger than D9
• D2.5 is equal to Q1 and D7.5 is equal to Q3
• Percentiles


  Score points that divide the data into 100 equal parts
• Nth percentile, Pn


  Separates the lowest n% from the other (100-n)%
• Mendenhall and Sincich Method


  A method that can be used in calculating quartiles
• Finding measures of position

  1. Arrange the values in the distribution in ascending order

  2. (a) Find the position of Q1 by using ¼ (n + 1) where n is the number of values

  3. (b) Find the position of Q2 by finding the median

  4. (c) Find the position of Q3 by using 3/4 (n + 1) where n is the number of values
• Q1


  The value that falls under the computed position of Q1
• Q2


  The value of the median
• Q3


  The value that falls under the computed position of Q3
• Finding deciles


  Similar to finding quartiles except the formula used in finding its positions
• Finding percentiles


  The ninety-nine score points which divide a distribution into one hundred equal parts
• Computing quartiles of grouped data

  Use the formula: Qk = LB + ((kN/4 − cfb) /fQk ) i where: LB =lower boundary of the Qk class, N =total frequency, Cfb =cumulative frequency of the class before the Qk class, fQk =frequency of the Qk class, I =size of class interval, K = nth quartile, where n=1, 2, and 3
• Grouped data


  • Class Interval, Frequency (f), Lower Boundary (LB), Cumulative Frequency (<cf)
• Finding Q1 for grouped data

  Q1 class = N/4, LB = 5.5, cfb = 6, fQ1 = 12, i = 5, Q1 = LB + ( (kN/4 − cfb) ÷ fQ1 (i), Q1 ≈ 8.21
• Finding D7 for grouped data

  D7 = LB + (7N/10 − cfb ÷ fD7) i, D7 ≈ 19.14
• Finding P65 for grouped data

  P65 = LB + (65N/100 − cfb ÷ fP65) i, P65 = 18
• Quartiles


  25% of the distribution has a value less than or equal to Q1, 50% or one-half of the distribution has a value less than or equal to Q2, 75% of the distribution has a value less than or equal to Q3
• Deciles


  10% of the distribution has a value less than or equal to D1, 20% of the distribution has a value less than or equal to D2, 30% of the distribution has a value less than or equal to D3
• Percentile


  1% of the distribution has a value less than or equal to P1, 2% of the distribution has a value less than or equal to P2, 3% of the distribution has a value less than or equal to P3
• Finding Q3 for ungrouped data

  • n = 10, Position of Q3 = 3/4 (n + 1) = 3/4 (10 + 1) = 3/4 (11) = 8.25, Q3 = 43
• Population


  The set of all possible values of a variable
• Sample


  Consists of one or more data drawn from a population
• Sampling


  Method of choosing a representative from a population
• Probability Sampling


  Involves random selection, allowing you to make strong statistical inferences about the whole group
• Non-probability Sampling


  Involves non-random selection based on convenience or other criteria, allowing you to collect data easily
• Measures of Central Tendency

  Sometimes called measures of central location
• Mean


  Often called the average; it is equal to the sum of all the values in the data set divided by the number of values in the data set
• Median


  The middle score for a set of data that has been arranged in order of magnitude
• Range


  The difference between the highest and the lowest values in a given set of data
• Interquartile Range


  The middle half of the data that is in between the upper and lower quartiles
• Variance


  Average squared difference of the values from the mean
• Standard Deviation


  Standard or typical difference between each data point and the mean