Representations of Data and Correlation

Scheme of work: Year 12 A-Level: Applied: Statistics: Representations of Data and Correlation

Prerequisite Knowledge

  • Interpret and construct frequency and grouped frequency tables,
  • Interpret and create cumulative frequency graphs, box plots and histograms.
  • Interpret, analyse and compare the distributions of data sets using the median, mean and interquartile range.
  • Use and interpret scatter graphs of bivariate data; recognise the correlation and know that it does not indicate causation;

Success Criteria

  • Interpret diagrams for single-variable data, including an understanding that an area in a histogram represents the frequency
  • Connect grouped frequency tables to probability distributions
  • Interpret scatter diagrams and regression lines for bivariate data, including recognition of scatter diagrams which include distinct sections of the population
  • Understand informal interpretation of correlation
  • Understand that correlation does not imply causation
  • Be able to calculate standard deviation, including from summary statistics
  • Recognise and interpret possible outliers in data sets and statistical diagrams
  • Be able to clean data, including dealing with missing data, errors and outliers

Teaching Points

  • Box Plots
  • Advantages
    • Highlights outliers
    • It makes it easy to compare datasets using the median and interquartile range.
  • Disadvantages
    • Detailed analysis is not possible as data are grouped into quartiles.
  • Cumulative Frequency Graphs
  • Advantages
    • Possible to estimate values within groups.
  • Disadvantages
    • It does not always highlight outliers
  • Histograms
  • Advantages
    • Clearly shows the shape of the distribution
  • Disadvantages
    • It does not always highlight outliers
    • Difficult to calculate quartiles.
    • When drawing and interpreting scatter graphs, the explanatory or independent variable goes on the x-axis, and the response or dependent variable goes on the y-axis.
    • When drawing histograms, a continuity correction involves changing the endpoints of an interval to the lower and upper bounds of the rounded data.

Common Misconceptions

  • When calculating the mean of grouped data, some students may divide by the number of groups rather than the number of data items.
  • When finding the standard deviation, students forget to take the square root.
  • Some students waste time by ignoring given values and recalculating ∑fx and ∑fx2.
  • Students often forget about the effect that coding data has on the variance.
  • Students often forget to calculate the mean and standard deviation of grouped data using the statistics mode on their calculator and prefer to work it out

Representations of Data and Correlation Resources

Mr Mathematics Blog

Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods

T- Formulae

Scheme of work: A-Level Further Mathematics: Further Pure 1: The t – formulae

Regression, Correlation and Hypothesis Testing

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Statistics: Regression, Correlation and Hypothesis Testing