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1. Data, Graphical Descriptive Techniques
Introduction
Descriptive statistics involves the arrangement, summary, and presentation of data to enable meaningful interpretation and to support decision making. Descriptive statistics methods make use of graphical techniques numerical descriptive measures The methods presented apply to both the entire population the population sample
Types of data
A variable is a characteristic of population or sample that is of interest for us, for instance, Cereal choice Capital expenditure The waiting time for medical services Data - the actual values of variables Quantitative data are numerical observations Qualitative data are categorical observations Quantitative data Age - income 55 75000 42 68000
.. .. Weight gain
. .
Qualitative data Person Married/unmarried 1 yes 2 no 3 no
.. .. Professor Rank 1 Lecturer 2 Full 3 Assistant .. .. With qualitative data, all we can do is to calculate the proportion of data that falls into each category. Lecturers Assistant Associate Full Total 15 25 5 15 60 25% 41.67 8.33% 25% 100% Knowing the type of data is necessary to properly select the technique to be used. Type of analysis allowed for each type of data Quantitative data - arithmetic calculations Qualitative data - counting the number of observation in each category Cross-sectional and Time-Series Data Cross-sectional data is collected at a certain point in time, for example, Marketing survey (observe preferences by gender, age) Test score in a statistics course Starting salaries of an MBA program graduates Time series data is collected over successive points in time, for instance, Weekly closing price of gold Amount of crude oil imported monthly
Relative Frequency It is often preferable to show the relative frequency (proportion) of observations falling into each class, rather than the frequency itself. Class relative frequency = Class frequency/Total number of observations Relative frequencies should be used when the population relative frequencies are studied comparing two or more histograms the number of observations of the samples studied are different Class width It is generally best to use equal class width, but sometimes unequal class width are called for. Unequal class width is used when the frequency associated with some classes is too low. Then, several classes are combined together to form a wider and “more populated” class It is possible to form an open ended class at the higher end or lower end of the histogram Shapes of histograms There are four typical shape characteristics Symmetry
Skewness
Positively skewed
Negatively skewed
Bell shaped histogram
Many statistical techniques require that the population be bell shaped.
Drawing the histogram helps verify the shape of the population in question
Stem and Leaf Display
This is an interval-scaled display, most useful in preliminary analysis. Stem and leaf diagram shows the value of the original observations (whereas the histogram “loses” them). Creating a stem and leaf display Observe the data in the table below 19.1 19.8 18.0 19.2 19.5 17.3 20.0 20. 19.6 18.5 18.1 19.7 18.4 17.6 21.2 20. 22.2 19.1 21.1 19.3 20.8 21.2 21.0 18. 19.9 18.7 22.1 17.2 18.4 21. Determine what constitutes a stem and a leaf (there is more than one way). For example:
the digits to the left of the decimal point is the stem
the digits to the right of the decimal point is the leaf
List the stems in a column from smallest to largest. Place each leaf at the same row as its stem. The complete display is: Stem Leaf 17 623 18 4705147 19 1983627571 20 038 21 12204 22 12 Conclusions from the stem and leaf display.
The observations range from 17.2 to 22.2.
Most of the observations fall between 18.0 and 20.0.
The shape of the distribution is not symmetrical.
Half the observations are below 19.5 and half above it.
Pie Charts, Bar Charts, Line Charts
