Further Maths Univariate Data

Univariate meaning: One variable. One quantity that changes. For example, number of cars sold by a car salesman Univariate meaning: One variable. One quantity that changes. For example, number of cars sold by a car salesman Type of data: Numerical and Categorical data. Type of data: Numerical and Categorical data. Interpreting the data: Discrete and continuous Interpreting the data: Discrete and continuous

Stem Plots One way of displaying data-how the data is distributed. One way of displaying data-how the data is distributed. Use this method if there are 50 (or less) observations Use this method if there are 50 (or less) observations Consist of two parts - a stem and a leaf, is always the last digit. Consist of two parts - a stem and a leaf, is always the last digit. Important!!!! Must always arrange the data in ascending first (not necessarily if using the graphic calculator) Important!!!! Must always arrange the data in ascending first (not necessarily if using the graphic calculator)

The stem may be broken into halves or fifths if the data are bunched up closely. The stem may be broken into halves or fifths if the data are bunched up closely. The stem plot need to include a key (similarly like a legend) The stem plot need to include a key (similarly like a legend)

Frequency histograms, dot plots and bar charts Other alternatives to display data, but larger data sets (50 or over observations) Other alternatives to display data, but larger data sets (50 or over observations) Frequency histograms and bar charts are like column graphs, very similar except that one is separated by a small equally space. Frequency histograms and bar charts are like column graphs, very similar except that one is separated by a small equally space. Note: This course relies reasonably on the use of the graphic calculator – LEARN HOW TO USE IT!!!! Note: This course relies reasonably on the use of the graphic calculator – LEARN HOW TO USE IT!!!!

Segmented bar charts A single bar to represent all the data being studied. A single bar to represent all the data being studied. The information is presented as percentages and so the total bar length represents 100% of the data. The information is presented as percentages and so the total bar length represents 100% of the data.

Describing the shape of stem plots and histograms Symmetric distributions Symmetric distributions Skewed distributions Skewed distributions

Distribution The spread of the data The spread of the data Symmetric distribution (single peak and the data trial off on both sides of this peak in roughly the same fashion) Symmetric distribution (single peak and the data trial off on both sides of this peak in roughly the same fashion)

Negatively Skewed Negatively Skewed The data peak to the right and trial off to the left The data peak to the right and trial off to the left

Positively Skewed Positively Skewed The data peak to the left and trail off to the right The data peak to the left and trail off to the right

Example Example Positively skewed

Example Example Symmetric distribution Most students receive about $8

Example Example Positively skewed distribution This indicates that most workers do up to 3 hours of exercise per week. Very few do more and the most time spent is 8 hours.