Minor Maths

1. Scatter Diagrams

   Annotations:

   • common sense and care are needed when interpreting the scatter diagrams. 1) Mathematically they may appear to be a relationship, but this does not imply that there is a relationship in reality. 2) The appearance of a mathematical relationship does not imply that there is a casual relationship. An increase in one variable does not necessarily cause an increase or a decrease in the other variable.
   1. Bivariate data

      Annotations:

      • Data connecting two variables are known as bivariate data
   2. Dependent Independent variables
      1. Independent data

         Annotations:

         • if one of the variables has been controlled , it is called the independent or explanatory variable
      2. Dependent data

         Annotations:

         • The other variable is then dependent or response variable
2. Regression function

   Annotations:

   • Having drawn a scatter diagram, you can then look for a mathematical relationship between the variables, y = f(x), where the function of f, known as the regression function
   1. Linear correlation and regression lines

      Annotations:

      • Simplest type of regression function, where y = f(x) is a straight line. If the points on the scatter diagram appear to lie near a straight line, called a regression line. You would say that there is linear correlation between x and y.
      1. Positive linear correlation

         Annotations:

         • y tends to increase as x increases
      2. Negative linear correlation

         Annotations:

         • y tends to decrease as x increases
      3. No correlation

         Annotations:

         • no relationship between x and y

Annotations:

• The standard deviation (s) is very important and useful measure of spread. It gives a measure of the deviations of the readings from the mean

1. calculations

   Annotations:

   • 1) for each reading x, calculate x-mean (its deviation from the mean) 2) square this deviation to give (x-mean)^2. (note that irrespective whether the deviation is negative or positive, this is now positive. 3) find sum of (x-mean)^2 4) find the average by dividing the sum by n, the number of readings. This gives variance. 5) Finally take the positive square root of the variance to obtain the standard deviation.