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

- 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;

- 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

**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.

- 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 ∑*fx*^{2}. - 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

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