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neurologyYou need to know

• On a scatter graph, each point represents a paired measurement `(x, y)` with the explanatory (independent) variable on the horizontal axis and the response (dependent) variable on the vertical axis.
• Correlation describes the direction and strength of a linear relationship: positive correlation means `y` tends to increase as `x` increases, negative correlation means `y` tends to decrease as `x` increases, and no correlation means there is no linear trend.
• A line of best fit on a scatter graph is a straight line drawn by eye that follows the overall trend so that points are roughly balanced above and below the line.
• Interpolation is estimating a value within the range of the observed `x`-values and is usually reliable; extrapolation is predicting beyond the data range and is less reliable because the trend may not continue.
• Correlation does not imply causation; a strong association between two variables does not prove that changes in one cause changes in the other.
• An outlier on a scatter graph is a point that lies far from the overall pattern and can distort the apparent trend and any predictions.
• A conversion graph for a direct proportion is a straight line through the origin with gradient equal to the conversion rate (for example, the number of kilometres per mile).
• On a conversion graph, corresponding values in the two units lie on the line; reading across and down (or vice versa) converts between units when axes are correctly labelled and scaled.
• A frequency tree shows how a total splits across categories; the frequencies on branches from a node add to the parent total, and all end-branches sum to the overall total.
• Probabilities from a frequency tree are found by ` ext{probability} = rac{ ext{relevant frequency}}{ ext{total frequency}}`, and conditional probabilities use the branch total as the denominator.
• In a time series line graph, time is plotted on the horizontal axis at equal intervals, the measured quantity on the vertical axis, and points are joined in chronological order to show trends over time.
• A stem-and-leaf diagram separates each number into a stem and a leaf, orders the leaves on each stem, and includes a key that explains how to read the values.
• From a stem-and-leaf diagram, the mode is the most common value, the median is the middle value in the ordered list, the range is ` max − min`, and the mean is ` \text{sum of values} ÷ \text{number of values}`.
• A frequency polygon is drawn by plotting each class midpoint against its frequency and joining adjacent points with straight line segments; for ungrouped discrete data, plot each distinct value against its frequency.
• For grouped data, the class midpoint is `\frac{\text{lower boundary} + \text{upper boundary}}{2}`, and the total frequency is the sum of class frequencies.
• A cumulative frequency table records the running totals up to each upper class boundary, and a cumulative frequency graph (ogive) plots cumulative frequency against the upper class boundary.
• On a cumulative frequency graph, the median is read at `50\%` of the total, the lower quartile `Q1` at `25\%`, the upper quartile `Q3` at `75\%`, and the interquartile range is `Q3 − Q1`.
• A box plot displays the five-number summary (minimum, `Q1`, median, `Q3`, maximum); the box spans `Q1` to `Q3` and whiskers extend to the minimum and maximum.
• Comparing two box plots on the same scale involves comparing medians for central tendency and interquartile ranges (or ranges) for spread, and commenting on any differences in skew or variability.
• In a histogram, bars touch to represent continuous data and the area of each bar is proportional to frequency, with height given by `\text{frequency density} = \dfrac{\text{frequency}}{\text{class width}}`; for equal class widths, heights are proportional to frequencies.

• Plot paired data on a correctly scaled scatter graph with clearly labelled axes and accurately positioned points.
• Draw an estimated line of best fit by eye so that points are roughly balanced above and below, then use it to interpolate a `y` for a given `x` within the data range or to estimate `x` for a given `y`.
• Make predictions from a scatter graph by interpolation or, if extending the line, by extrapolation, and explicitly comment on the reliability of the estimate and that correlation does not imply causation.
• Construct a conversion graph from given pairs (for direct proportion, a straight line through the origin), label units and scales, and use the graph to convert values in both directions to a specified degree of accuracy.
• Draw a frequency tree from given totals, percentages, or part-frequencies, complete missing branch and total frequencies, and calculate simple and conditional probabilities from the tree.
• Create a time series line graph from a table by placing time at equal intervals on the horizontal axis, plotting values, joining points in order, and describing short-term changes and overall trend.
• Construct a stem-and-leaf diagram with ordered leaves and a clear key, then calculate the mode, median, mean, and range directly from the display.
• Draw a frequency polygon for grouped data by calculating class midpoints, plotting midpoint–frequency pairs, joining with straight lines, and labelling axes; for ungrouped data, plot each value (or distinct value with its frequency).
• Produce a cumulative frequency graph by forming a cumulative frequency table, plotting cumulative frequencies at upper class boundaries, drawing a smooth ogive, and reading the median, quartiles, and interquartile range from the graph.
• Construct a box plot from a five-number summary (or from values read off a cumulative frequency graph) on a correctly scaled axis, and compare two box plots on the same scale by commenting on differences in median and interquartile range as evidence of centre and spread of distributions.