descriptive statistics

• Descriptive statistics


  Statistics that summarize and describe certain features of data.
• Measures of central tendency


  • A single value that summarises a set of data by identifying the typical value of the data set, also known as an average.
  • Mean
  • Median
  • Mode
• Mean


  The arithmetic/mathematical average, calculated by adding all the values and then dividing by the number of values.
• Median


  The value in the central position of a data set. The median is calculated by ordering the values from lowest to highest and selecting the value in the middle. If there are an even number of data points, then the median is the halfway point between the two centre values.
• Mode


  The most frequent score in a quantitative data set. If there are two modes, the data is bi-modal, and if there are more than two modes, the data set is multi modal.
• Measures of dispersion


  • A single value that summarises the spread of a set of data
  • Range
  • Standard deviation
• Range


  The range is the difference between a data set's highest and lowest values. To calculate the range subtract the smallest value in the data set from the largest.
• Standard deviation


  The standard deviation is a complex calculation using all data points that produces a single value.

  It shows how much variation there is from the "average" (mean). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
• Percentage


  A way of describing data, calculated by dividing a number by the total and multiplying by 100.
• Calculating percentage change


  Subtract the new number from the old number, divide by the old number, then multiply by 100.

  e.g. Year 1 = 595 Year 2 = 724

  724-595/595 x 100
• Evaluation of mode

  Strengths: the mode is not distorted by extreme scores called outliers.

  The mode is helpful for discrete numbers; for example, it can make more sense to say the average family has two children that 1.89 children.

  Limitations: There can be no modes if every value is different or multiple modes; this is especially likely in small data sets. This means in some cases, the mode does not give an exact average value.
• Evaluation of median

  Strengths: as the median is the central value, its calculation is not affected by extreme outlier scores.

  The median is very easy to calculate.

  Limitations: The median score does not include all of the values in its calculation, so it is not as sensitive as the mean measure of central tendency.

  If there are an even number of data points, unlike the mode, the 'typical' value will be a number that is not one of the recorded values.
• Evaluation of Mean

  Strengths: all raw data points are used (represented) in calculating the mean. This means the mean is the most sensitive measure of central tendency.

  Limitations: due to the sensitivity of the mean, the mean is distorted by extremely high or law value (outliers)
• Evaluation of range

  Strengths: the range is easy to calculate, especially compared to the alternative measure of dispersion, the standard deviation.

  Limitations: extreme scores easily disort the value.

  The range does not show if the scores are clustered around the mean or more evenly spread out.
• Evaluation of standard deviation

  Strengths: The SD includes all values in its calculation, making it more sensitive than the range.

  The SD provides information about the spread of scores.

  Limitations: Extreme scores also disort the SD.

  The SD is significantly more difficult to calculate than the range.