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neurologyYou need to know

• A scatter diagram plots paired data as points on a coordinate grid with both axes labelled with the variables and their units.
• Correlation on a scatter diagram can be positive, negative, or zero, and the closer the points lie to an imagined straight line the stronger the correlation.
• A line of best fit is a straight line drawn through a scatter diagram to model the trend and should have roughly equal numbers of points above and below it.
• Interpolation uses the line of best fit to predict values within the observed range of the horizontal variable, whereas extrapolation predicts beyond this range and is less reliable.
• Correlation does not imply causation; two variables may be correlated due to a lurking third variable or coincidence rather than a cause–effect link.
• A conversion graph for a proportional relationship is a straight line through the origin whose gradient equals the conversion rate (for example, kilometres per mile).
• To use a conversion graph you read from a value on one axis to the conversion line and then to the other axis to obtain the corresponding value.
• A frequency tree shows how a total splits into categories along branches, with the frequencies on branches from a node adding to the parent total and the leaf totals adding to the overall total.
• A time series line graph places time on the horizontal axis and connects values in chronological order to reveal trends, peaks, and troughs.
• A stem-and-leaf diagram separates each data value into a stem and a leaf, orders all leaves, includes a key showing place value, and preserves the original data values.
• From ordered data (or a stem-and-leaf diagram): the mode is the most frequent value, the median is the middle value, the range is maximum minus minimum, and the mean is `\bar{x} = \frac{\sum x}{n}`.
• A frequency polygon plots frequency against the class midpoint for each class interval and joins the points with straight lines, allowing multiple datasets to be compared on the same axes.
• A cumulative frequency graph plots less-than cumulative frequency against the upper class boundary and typically forms a smooth, increasing (ogive) curve.
• On a cumulative frequency graph, the median is read at `\frac{n}{2}`, the lower quartile at `\frac{n}{4}`, the upper quartile at `\frac{3n}{4}`, and the interquartile range is `\text{IQR} = Q_3 - Q_1`.
• A box plot displays the five-number summary (minimum, lower quartile, median, upper quartile, maximum), with the box length equal to the IQR and whiskers extending to the minimum and maximum values.
• When comparing box plots, differences in medians show shifts in typical values while differences in IQRs show differences in spread, and the IQR is resistant to extreme values unlike the range.
• In a histogram with unequal class widths, the vertical scale is frequency density with `\text{frequency density} = \frac{\text{frequency}}{\text{class width}}`, bars touch to indicate continuous data, and bar area is proportional to frequency.
• When class widths are equal, using frequency or frequency density produces the same histogram shape because class width is constant for all bars.
• The modal class is the class with the largest frequency; in histograms with unequal widths it cannot be identified by the tallest bar alone because bar height shows density, not frequency.

• Plot a scatter graph for a bivariate dataset by choosing sensible linear scales, labelling axes with variables and units, and plotting each data pair accurately to the nearest grid square, then describe the correlation’s direction and strength in context.
• Draw a line of best fit by eye so that points are balanced above and below, and use it to estimate a missing value by reading across to the line and then to the other axis, stating when an estimate is an interpolation (safer) or an extrapolation (less reliable).
• Draw a conversion graph from at least two known pairs (including the origin for proportional conversions), sketch a straight line with correct gradient, and use it to convert values with appropriate accuracy from one unit to another.
• Construct and complete a frequency tree by writing frequencies on branches that sum correctly at each node, checking that the totals at the leaves equal the overall total, and using the tree to read off category counts and proportions.
• Plot a time series line graph from a table by placing equal time intervals on the horizontal axis, plotting values, and joining points in order to show trend, peaks, and troughs.
• Draw a stem-and-leaf diagram by selecting suitable stems, ordering all leaves, and writing a clear key, then find the mode, median, range, and mean from the display.
• Draw a frequency polygon from grouped data by calculating class midpoints, plotting (midpoint, frequency) points to a consistent scale, and joining with straight lines; use shared axes to compare two datasets.
• Draw a cumulative frequency graph by calculating less-than cumulative totals, plotting them against upper class boundaries, sketching a smooth increasing curve, and reading off the median, quartiles, and `\text{IQR}`.
• Construct a box plot to scale from a five-number summary or from cumulative frequency estimates, and compare two box plots by commenting on differences in median (typical value) and IQR (spread).
• Construct a histogram for equal and unequal class intervals by calculating class widths and frequency densities, drawing touching bars on a continuous scale, and using the graph to estimate frequencies over intervals and comment on distribution shape.