stats 5

• Time Series Graphs


  A line graph with time plotted on the x-axis. Used to spot trends – usually going up or down or fluctuating (going up and down).
• Time series


  A set of data collected over a period of time at equal intervals – could be years, quarter, months or days.
• Trend Lines


  Shows the general trend of the data. When drawing trend lines ignore fluctuations and follow the general pattern (is the data going upwards or downwards)
• Trend line types


  • Rising (upwards) trend
  • Falling (downwards) trend
  • Level trend
• Moving Averages


  An average worked out for a given number of successive observations. A good way to see trends in data with large variations – they smooth out fluctuations and make the trend line more accurate.
• Plotting moving averages


  1. Plot at the midpoint of the time interval

  2. Do not join the up – use LOBF
• Moving average example


  • For 3 point moving average, 1st Value = (520+300+380)/3=400, Plot at middle of these 3 values so at Spring 2001
  • 2nd Value = (300+380+640)/3=430, Plot at Summer 2001
  • 3rd Value = (380+640+540)/3=520, Plot at Autumn 2001
  • 4th Value = (640+540+500)/3=560, Plot at Spring 2002
• Seasonal Variations


  Variations may be: A general trend – shown by the trend line, Seasonal Variations – a pattern that repeats at a specific point every cycle.
• Seasonal Variations in a time series follow a regular time period, like days of the week or seasons.
• Seasonal Variation at a point

  How much the value varies from the trend.
• Calculating Seasonal Variation at a point

  Seasonal Variation = Actual Value - Trend Value
• Estimated Mean Seasonal Variation (EMSV)

  The average of all the seasonal variations for the same point in each cycle.
• Calculating Estimated Mean Seasonal Variation

  EMSV = Mean of all the seasonal variations for that season
• Predicting Values


  Predicted Value = Trend Line Value (from graph) + EMSV