4.1.7 Interpreting Data

Interpreting Data

The mode is useful for qualitative data
- It is not as useful for quantitative data as there is not always a unique mode
The mean includes all values
- It is affected by outliers
- A smaller/larger mean is preferable depending on the scenario
  - A smaller mean time for completing a puzzle is better
  - A bigger mean score on a test is better
The median is not affected by outliers
- It does not use all the values
The range gives the full spread of the all of the data
- It is affected by outliers
The interquartile range gives the spread of the middle 50% about the median and is not affected by outliers
- It does not use all the values
- A bigger IQR means the data is more spread out about the median
- A smaller IQR means the data is more centred about the median
The standard deviation and variance use all the values to give a measure of the average spread of the data about the mean
- They are affected by outliers
- A bigger standard deviation means the data is more spread out about the mean
- A smaller standard deviation means the data is more centred about the mean

Box plots
- Can be used with ungrouped univariate data
- Shows the range, interquartile range and quartiles clearly
- Very useful for comparing data patterns quickly
Cumulative frequency graphs
- Can be used with continuous grouped univariate data
- Shows the running total of the frequencies that fall below the upper bound of each class
Histograms
- Can be used with continuous grouped univariate data
- Used with equal class intervals
- Shows the frequencies of the group
Scatter diagrams
- Can be used with ungrouped bivariate data
- Shows the graphical relationship between the variables

Compare a measure of central tendency
- If the data contains outliers - use the median
- If the data is roughly symmetrical – use the mean
Compare a measure of dispersion
- If the data contains outliers - use the interquartile range
- If the data is roughly symmetrical – use the standard deviation
Consider whether it is better to have a smaller or bigger average
- This will depend on the context
  - A smaller average time for completing a puzzle is better
  - A bigger average score on a test is better
Consider whether it is better to have a smaller or bigger spread
- Usually a smaller spread means it is more consistent
Always relate the comparisons to the context and consider reasons
- Consider the sampling technique and the data collection method