What are the mean, mode and median?

• Mean, median and mode are?measures of central tendency
  • They describe where the centre of the data is
• They are all types of?averages
• In statistics it is important to be specific about which average you are referring to
• The?units?for the mean, mode and median are the?same?as the units for the data

How are the mean, mode, and median calculated for ungrouped data?

• The?mode?is the value that occurs?most often?in a data set
  • It is possible for there to be?more than one mode
  • It is possible for there to be?no mode
    • In this case?do not?say the mode is zero
• The?median?is the?middle?value when the data is in?order of size
  • If there are two values in the middle then the median is the?midpoint?of the two values
• The?mean?is the?sum?of all the values?divided by the number of values

• • The mean can be represented by the symbol?μ
• Your?GDC?can calculate these statistical measures if you input the data using the statistics mode

What are quartiles?

• Quartiles?are?measures of location
• Quartiles?divide a population?or data set?into?four equal sections
  • The?lower quartile,?Q₁?splits the lowest 25% from the highest 75%
  • The?median,?Q₂?splits the lowest 50% from the highest 50%
  • The?upper quartile,?Q₃?splits the lowest 75% from the highest 25%
• There are different methods for finding quartiles
  • Values obtained by hand and using technology may differ
• You will be expected to use your GDC to calculate the quartiles

What are the range and interquartile range?

• The?range?and?interquartile range?are both?measures of dispersion
  • They describe how spread out the data is
• The?range?is the largest value of the data minus the smallest value of the data
• The?interquartile range?is the range of the central 50% of data
  • It is the upper quartile minus the lower quartile

• • • This is given in the?formula booklet
• The?units?for the range and interquartile range are the?same?as the units for the data

What are the standard deviation and variance?

• The?standard deviation?and?variance?are both?measures of dispersion
  • They describe how spread out the data is in relation to the mean
• The?variance?is the?mean?of the?squares?of the?differences?between?the values and the mean
  • Variance is denoted σ²
• The?standard deviation?is the?square-root?of the?variance
  • Standard deviation is denoted σ
• The?units?for the standard deviation are the?same?as the units for the data
• The?units?for the variance are the?square?of the units for the data

How are the standard deviation and variance calculated for ungrouped data?

• In the exam you will be expected to use the statistics function on your?GDC?to calculate the standard deviation and the variance
• Calculating the standard deviation and the variance by hand may deepen your understanding

• You?do not?need to learn these formulae as you will use your GDC to calculate these