S-Cool Revision Summary

S-Cool Revision Summary

Data

There are 2 types of data:

  1. Qualitative - where the data is not numerical.
  2. Quantitative - where the data is numerical.

Quantitative data is the most useful set of data to us and can be in 2 forms:

  1. Discrete data - can only take certain values.
  2. Continuous data - this set of data can take any value within a given range.

Note: measuring will give us continuous data whereas counting will give discrete.

Averages

The mode is the most popular value or values, i.e. the piece or pieces of data that occur most often.

The median is the middle piece of data when the data is in numerical order.

In general, to find the place of the median of n pieces of data we can use the following 2 rules:

  1. n odd - then use ½(n + 1) (the value just over halfway).
  2. n even - we find halfway between ½n and the next value (halfway and the next value).

The mean of a set of data is the sum of all the values divided by the number of values.

The mean is denoted by and for n pieces of data is calculated by:

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just means the sum of all the x's - for instance, add all the bits of data together.

Quartiles

The lower quartile is the value 25% (1/4) of the way through the distribution.

The upper quartile is the value 75% (3/4) of the way through the distribution.

The median is the value 50% (1/2) of the way through the distribution.

Standard deviation

The standard deviation gives a measure of how the data is dispersed about the mean, the centre of the data.

There are 2 formulae for calculating the standard deviation, .

Formula 1 =

Formula 2 =

The variance is the square of the standard deviation.

Variance =