yr1 chap 3 representations of data

• an outlier is an extreme value which is outside the overall pattern of data
• there are lots of different ways to define an outlier, but they have to tell you which method to use in the exam
• box plots are diagrams which show the median, upper quartile, lower quartile, maximum, minimum and any outliers
• outliers are shown on a box plot by a cross or asterisk
• interquartile range is the difference between the upper quartile and lower quartile
• cumulative frequency diagrams can be drawn from data in a grouped frequency table to find estimates for the median, quartiles and percentiles
• a cumulative frequency diagram has cumulative frequency on the y axis and whatever the variable is on the x axis
• histograms are diagrams to represent grouped continuous data
• in a histogram, the area of the bar is proportional to the frequency of each class, the formula is:

  area of bar = k x frequency
• in a histogram, if area of bar = k x frequency, and k = 1, the formula for frequency density is:

  frequency density = frequency / class width
• if you join the middle of the top of each bar in a histogram, you get a frequency polygon
• a histogram has frequency density on the y axis and whatever the variable is on the x axis
• when comparing data sets, either talk about a measure of location, or a measure of spread

  you can use the mean and the standard deviation, or the median and the interquartile range

  you cannot use the median and the standard deviation, or the mean and the interquartile range
• if a box plot has a low median, you would expect the data to have a low mean

  if a box plot has a high median, you would expect the data to have a high mean
• if a box plot has a low IQR, you would expect the standard deviation to be small

  if a box plot has a high IQR, you would expect the standard deviation to be large