quantitative data & analysis

• measure of central tendency

  mean, median & mode
• mean

  sum of all the values in a data set divided by the number of values

  represents the average
• strength of the mean

  uses all data points, providing a comprehensive measure of central tendency
• weakness of the mean

  sensitive to outliers which can skew the result
• median

  middle value of the data set when values are arranged in order

  if there is an even number of value the median is the average of the 2 middle numbers
• strength of the median

  not affected by outliers, making it a better measure for skewed distributions
• weakness of the median

  doesn’t take into account the value of all data points
• mode

  value/ values that appear most frequently in a data set

  a set can have more than one mode (bimodal/ multimodal) or no mode at all
• strength of the mode

  useful for identifying the most common value in a set
• weakness of the mode

  may not provide useful info if data set has no repeating values or multiples
• measure of dispersion

  range & standard deviation
• range

  difference between the highest and lowest values in a data set
• strength of the range

  simple to calculate and understand & provides quick sense of data spread
• weakness of the range

  sensitive to outliers (a single extreme value can significantly affect the range)
• standard deviation

  average if the squared differences from the mean
• strengths of standard deviation

  takes into account all data points, providing a comprehensive measure of spread

  useful in further statistical analyses
• weaknesses of standard deviation

  can be difficult to interpret since variance is in squared units of the original data

  sensitive to outliers which can inflate the variance
• how to calculate standard deviation

  find mean of data set

  subtract mean from each data point & square the result

  calculate the average of the squared differences

  take the square root of the average to obtain the standard