maths stats definitions

• Mode


  The most common or most popular data value
• Mode


  • Can be used for qualitative data
  • Not suitable if the data values are very varied
• Mean


  Important as it uses all the data values
• Mean


  • Disadvantage – affected by extreme values
• Median


  The middle value when the data are in order
• For n data values the median is the n + 1th value
• Median


  • Not affected by extreme values
• Range


  Biggest value – smallest value
• Range


  • Greatly affected by extreme values
• Interquartile Range (IQR)


  Upper quartile – Lower quartile
• Interquartile Range (IQR)


  • Measures the spread of the middle 50% of the data and is not affected by extreme values
• Interquartile Range (IQR)


  • 9 - 4 = 5
  • 7.5 – 3.5 = 4
• Standard Deviation


  • Deviation from the mean is the difference from a value from the mean value
  • The standard deviation is the average of all of these deviations
• Formulas to work out standard deviation are given in the
• If you add a to each number in the list of data


  • New mean = old mean + a
  • New median = old median + a
  • New mode = old mode + a
  • Standard Deviation is UNCHANGED
• If you multiply each number in the list of data by b


  • New mean = old mean × b
  • New median = old median × b
  • New mode = old mode × b
  • New Standard Deviation = old standard deviation × b
• If the data is grouped – use the mid-point of each group as your x
• For 10 values the median will be the 5½ th value – halfway between the 5th and the 6th values
• Outcome: each thing that can happen in an experiment
• Sample Space


  List of all the possible values
• A and B both happen

  A Ç B
• Either A or B or both happen

  A È B
• P(C') = 1 – P(C)
• Mutually Exclusive Events


  Two or more events that cannot happen at the same time
• Independent Events


  The outcome of one event does not affect the outcome of another
• P(B) = P(A) P(B)
• Conditional Probability


  When the outcome of the first event affects the outcome of a second event, the probability of the second event depends on what has happened
• P(B/A) means the conditional probability of B given A
• P(B/A) = P(A Ç B) / P(A) so P(A Ç B) = P(A) P(B/A)
• If the question states that the events are independent then a tree diagram might be a good idea – multiply along the branches then add the appropriate combinations together
• Probability of 'at least 1' = 1 – Probability of 'none'
• If you are asked to find probabilities using data in a table – work out the row/column totals before you start
• Binomial Distribution


  A question is binomial if: Probability of an event happening is given (p), Number of people/trials/objects chosen given (n)
• EQUALS or EXACTLY use the formula P(x=r)
• MORE/LESS THAN/AT LEAST use tables
• Tables give less than or equal to
• P(X>5) = 1 – P(X≤5)
• P(X<5) = P(X ≤ 4)
• Binomial Distribution


  • Independent events with a fixed probability of success
  • Randomly selected
• You may be asked to calculate the mean and standard deviation of a binomial distribution and compare them to the mean and standard deviation of a sample (table of results) - if both the means are approximately the same AND both standard deviations (or variances) are approximately equal then you can say that binomial model appears to fit the data and that it must be independent, random observations.