What are mean, median and mode?

• Mean, median and mode are measures of?location
  • A measure of location gives information about where data is in the number system
  • 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

How are mean, median and mode calculated?

• You should already be familiar with finding the mean, median and mode from raw, ungrouped data
• The?mode?is the value that occurs?most often?in a data set
  • In a frequency table the?group?or?class?that occurs most often will be referred to as the?modal class
  • A data set with more than one mode is?bimodal
• The?median?is the?middle?value when the data is in?order of size
  • If there are two values in the middle of the data set, the median is the?midpoint?of the two values
  • If finding median from a?frequency table?find the cumulative frequency first and find the group or class where the middle value will lie
  • You?may have to use?linear interpolation?when finding the median from a?grouped frequency table
• The?mean?is the?sum?of all the values?divided by the number of values?in the data set

What are summary statistics and their notation?How do we choose the best measure of central tendency?

• It is often better to use one of the averages over the others, depending on the data set
  • It’s a good idea to be aware of the advantages and disadvantages of the use of each average
• The mean uses all of the data values, this is good for a large data set where all of the values are close together, but also means that the mean can be affected by extreme values
• The median is not affected by very high or low values so is a good average to use in data sets with extreme values
• The mode is very useful in a lot of practical situations, however often there may be more than one mode, no mode or even a mode that is nowhere near the middle of the data set

What are quartiles and percentiles?

• Quartiles and percentiles?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,?is the value that is 50% of the way through the data
  • The?upper quartile, Q₃,?splits the lowest 75% from the highest 25%
• Percentiles?divide the data into 100 parts
  • The 70th percentile lies seven-tenths of the way through the data
    • 70% of the data is below it and 30% is above it

How are quartiles calculated?What are the range and interquartile range?

• The?range?and?interquartile range?are both?measures of spread
• A measure of spread gives information about how spread out the data set is
• The?range?is the difference between the?largest?and?smallest?values in the data set
  • All data points in the set will be included in the range, including?extreme values
• The?interquartile range?is the difference between the?upper quartile?and the?lower quartile
  • Only the middle 50% of the data is included in the interquartile range
  • It is not affected by extreme values
  • Sometimes?an interpercentile range could be asked for, this is the difference between two given percentiles
    • For example, the 20th to 80th interpercentile range would be the difference between the 80th percentile and the 20th percentile
• The units for range and interquartile range are the same as the units for the original data