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neurologyYou need to know

• The mode is the value or category with the greatest frequency.
• The range is calculated by subtracting the smallest value from the largest value.
• The median is the middle value when the data are placed in order.
• In a frequency table, the total frequency is the total number of data values in the set.
• In a frequency table, the position of the median is found using the total frequency; for an odd total frequency it is the middle item, and for an even total frequency it is halfway between the two middle items.
• A cumulative frequency is a running total of the frequencies up to and including each value or class interval.
• The mean from a frequency table is calculated using `\frac{\text{sum of each value multiplied by its frequency}}{\text{total frequency}}`.
• Grouped data are data collected into class intervals, so the exact original values are usually not known.
• A class interval has a lower boundary and an upper boundary, such as `10 \leq x < 20`.
• The median class is the class interval that contains the middle value of the grouped data.
• For grouped data, the median class is found using cumulative frequency and the position `\frac{n}{2}`, where `n` is the total frequency.
• The midpoint of a class interval is calculated using `\frac{\text{lower boundary}+\text{upper boundary}}{2}`.
• The estimated mean from grouped data is calculated using `\frac{\text{sum of each class midpoint multiplied by its frequency}}{\text{total frequency}}`.
• An estimated mean from grouped data is only an estimate because the exact values inside each class interval are unknown.
• Linear interpolation estimates a value inside a class interval by assuming the data are evenly spread across that interval.
• The median from grouped data can be estimated using `L+\frac{\frac{n}{2}-C}{f}\times w`, where `L` is the lower boundary of the median class, `C` is the cumulative frequency before the median class, `f` is the frequency of the median class, and `w` is the class width.
• The lower quartile is the value one quarter of the way through an ordered data set, and the upper quartile is the value three quarters of the way through an ordered data set.
• The interquartile range measures the spread of the middle half of a data set and is calculated using `\text{upper quartile}-\text{lower quartile}`.
• A larger range or interquartile range shows greater spread, while a smaller range or interquartile range shows more consistency.
• Averages such as the mean and median describe the centre of a distribution, while the range and interquartile range describe the spread of a distribution.

• Find the mode from a frequency table by identifying the value or category with the highest frequency.
• Calculate the range from a frequency table by subtracting the lowest value with a non-zero frequency from the highest value with a non-zero frequency.
• Find the median from a frequency table by using cumulative frequency to locate the middle item or items in the ordered data.
• Calculate the mean from a frequency table by multiplying each value by its frequency, adding these products, and dividing by the total frequency.
• Identify the median class in grouped data by calculating cumulative frequencies and finding the first class interval that reaches or passes `\frac{n}{2}`.
• Estimate the mean from grouped data by finding each class midpoint, multiplying each midpoint by its frequency, adding the products, and dividing by the total frequency.
• Use linear interpolation to estimate the median from grouped data by substituting the lower boundary, cumulative frequency before the class, class frequency, class width and total frequency into the median formula.
• Find the lower quartile, upper quartile and interquartile range from an ordered data set, using appropriate quartile positions and subtracting lower quartile from upper quartile.
• Compare two distributions by commenting on both their average and their spread, using values such as the mean, median, range or interquartile range to support the comparison.