Statistics

Traps in Statistics

• Calculates a different quantity
  Name the quantity and its unit before you start (remainder; horizontal distance; cm²). After calculating, check your number is that quantity and not a neighbour.
• Applies the rule for a different situation
  Identify the situation first (angle at centre? opposite angles of a cyclic quadrilateral? reverse bearing?) and write the rule that belongs to it before calculating.
• Confuses mean, median, mode and range
  Mean = sum ÷ count. Median = middle value of SORTED data. Mode = most frequent. Range = largest − smallest.
• Finds the median without sorting
  Always sort first. Odd count → middle value. Even count → average of the two middle values.
• Careless calculation
  Not a knowledge gap — a checking gap. Re-read the question, estimate the answer first, and check every line before you choose an option.
• Gives the median's position instead of its value
  (n + 1)/2 tells you WHERE the median is in the sorted list; the median is the VALUE found there. Sort, count to that position, read off the value.
• Goes one step too far
  Match the quantity to its definition: variance = mean of squared deviations; SD = √variance; IQR = Q₃ − Q₁; semi-IQR = ½(Q₃ − Q₁). Stop at the one the question names.
• Stops one step short of the answer
  Before writing the answer, re-read the question's last words (each angle? neither? Ama's share? variance?). Ask: is my number that thing, or a stage on the way to it?
• Is off by one in counting
  For the nth term there are n − 1 gaps between the 1st and nth terms. For quartiles, use the (n + 1)/4 and 3(n + 1)/4 positions and count carefully.
• Uses the wrong operation
  Write the rule in words first (bearing back = bearing ± 180°; IQR = Q₃ − Q₁), then substitute. Estimate: does the size of the answer make sense?