descriptive statistics

• descriptive statistics


  provide a summary of a set of data, drawn from a sample, that applies to a whole target population

  • they include measures of central tendency and measures of dispersion
• measures of central tendency

  used to summarise large amounts of data into averages

  there are 3 types:

  • median
  • mode
  • mean
• median


  the median is the central score in a list of rank-ordered scores

  advantages:

  • it is not effected by extreme scores
  • it is usually easier to calculate than the mean
  • the median can be used with ordinal data, unlike the mean

  disadvantages:

  • it is not as sensitive as the mean because not all the scores are used in the calculation
  • it can unrepresentative in a small set of data
• mean


  the mid-point of the combined values of a set of data

  advantages:

  • it is the most accurate measure of central tendency as it uses the interval level of measurement, where the units of measurement are of equal size
  • uses all of the data in calculation

  disadvantages:

  • it is less useful if some scores are skewed, such as if there are some large or small scores
  • the mean score may not be one of the actual scores in the set of data
• mode


  the most common number in a set of scores

  advantages:

  • it is less prone to distortion by extreme values
  • it sometimes makes more sense than the other measures

  disadvantages;

  • there can be more than one mode in set of data
  • it does not use all the scores
• measures of dispersion


  provide measures of the variability of scores.

  they include:

  • the range
  • interquartile range
  • standard deviation
• the range


  calculated by subtracting the lowest value from the highest value ina set of data

  advantages:

  • fairly easy and quick to work out
  • takes full account of extreme values

  disadvantages:

  • it can be distorted by extreme values
  • does not show whether data are clustered or spread evenly around the mean
• standard deviation


  measure of the variability of a set of scores from the mean. the larger the standard deviation the larger the spread of scores will be.

  standard deviation is calculated by:

  • add all the scores together and divide by the number of scores to calculate
  • subtract the mean from each individual score
  • square each of these scores
  • add all the squared scores together
  • divide the sum of the squares by the number of scores minus 1. this is the variance
  • use calculator to work out the square root of the variance - standard deviation
• standard deviation - advantages and disadvantages

  advantages:

  • it is a more sensitive dispersion measure than the range since all scores are used in its calculation
  • it allows for the interpretation of individual scores

  disadvantages:

  • it is more complicated to calculate
  • it is less meaningful if data are not normally distributed
• presentation of quantitative data

  quantitative data can be presented in various ways, for example:

  • bar charts (not continuous)
  • histograms (continuous)
  • frequency polygon (line graph) (continuous)
  • pie charts
• normal distribution


  for a given attribute most scores will be on or around the mean, with decreasing amounts away from the mean

  • data is symmetrical, normally forms a bell-shaped curve when plotted (equal amount of scores above and below the mean)

  several ways to check if data is normally distributed:

  • examine visually: look at the data to see if most scores are clustered around the mean
  • calculate measures of central tendency: calculate the mean, mode and median to see if they are similar
  • plot the frequency distribution: plot the data on a histogram to see if it forms a bell-shaped curve
• skewed distribution


  unless data is symmetrical it will be skewed

  • anomalies can cause skewed distributions
  • a positive skewed distribution occurring when there is a high extreme score
  • a negative skewed distribution occurring when there is a low extreme score
  • positively skewed distribution will contain more low than high scores
  • negatively skewed distribution will contain more high than low scores
  • if mean is lower than other 2 (median and mode) its negatively skewed
  • if mean is higher than other 2 its positively skewed
• graphs


  bar charts:

  • categories and bards need to be separate (nominal categories)(words)

  histogram:

  • continuous data, bars together (numerical)

  frequency polygon:

  • line graph, good for comparing (numerical) (2 data sets)

  scatter graph:

  • correlation, relation, association