Comparing Data using Summary Statistics (College Board AP® Statistics)

Comparing data using summary statistics

• Any of the numerical summaries (e.g., mean, standard deviation, relative frequency, etc.)

  • can be used to compare two or more independent samples

How do I compare two data sets?

• You may be given two sets of data that relate to a context

• To compare data sets, you need to

  • compare their measures of center

    • Mode, median or mean

  • compare their measures of spread

    • Range, interquartile range or standard deviation

  • comment on the shape of the distribution of the data

    • Skew, symmetry

  • comment on any unusual features

    • Outliers (extreme values), gaps, clusters (groupings of data values), multiple peaks in the shape of the distribution

How do I write a conclusion when comparing two data sets?

• When comparing features, you need to

  • compare numerical values or calculate summary statistics

  • describe (interpret) what this means in real life 

• For example, some good ways to describe a measure of spread (variability) are:

  • "A smaller spread of scores means...

    • scores are closer together"

    • scores are more consistent"

    • there is less variation in the scores"

What restrictions are there when drawing conclusions?

• The data sets may be too small to be truly representative

  • Measuring the heights of only 5 pupils in a whole school is not enough to talk about averages and spreads

• The data sets may be biased

  • Measuring the heights of just the older year groups in a school will make the average appear too high

• The conclusions might be influenced by who is presenting them

  • A politician might select the specific type of average that helps to strengthen their argument!

• You may need to choose which measure of center or measure of spread to compare

  • Check for outliers (extreme values) in the data

    • If there are outliers, avoid using the mean, standard deviation and range as they are affected by extreme values!