# 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
• Highlights outliers
• It makes it easy to compare datasets using the median and interquartile range.
• Detailed analysis is not possible as data are grouped into quartiles.
• Cumulative Frequency Graphs
• Possible to estimate values within groups.
• It does not always highlight outliers
• Histograms
• Clearly shows the shape of the distribution
• 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