Key Points

The main purpose of classifying raw data is to arrange it systematically to bring order. This makes the data comprehensible and suitable for further statistical analysis.

Raw data is the unclassified, unorganized data collected in its original form. It is often large and difficult to interpret without proper organization.

Data can be classified in several ways, including Chronological (by time), Spatial (by location), Qualitative (by attributes like gender), and Quantitative (by numerical values like height or income).

A variable is a characteristic that can be measured and whose value changes over time or across different individuals or objects.

A continuous variable can take any numerical value within a range, including fractions (e.g., height). A discrete variable can only take specific, finite values and 'jumps' from one value to the next (e.g., number of students).

A frequency distribution is a table that summarizes quantitative data by grouping it into classes and showing the number of observations (frequency) that fall into each class.

Class Limits are the highest and lowest values of a class. Class Interval is the width of a class. Class Mark is the midpoint of a class, calculated as (Upper Limit + Lower Limit) / 2.

In the exclusive method, the upper limit of one class is the lower limit of the next (e.g., 10-20, 20-30). An observation equal to the upper limit is excluded from that class and included in the next.

In the inclusive method, both the lower and upper class limits are included in that class (e.g., 10-19, 20-29). This creates a gap between the upper limit of one class and the lower limit of the next.

To ensure continuity for continuous variables in an inclusive series, an adjustment is made. Half the gap between classes is subtracted from lower limits and added to upper limits.

Tally marking is a method to count frequencies for each class from raw data. Tallies are grouped in sets of five, where four are vertical lines and the fifth is a diagonal line across them.

Classification results in a loss of information because individual observations lose their identity. All values within a class are assumed to be equal to the class mark for further calculations.

A frequency array is the classification of a discrete variable. It lists each distinct value of the variable and its corresponding frequency.

A univariate frequency distribution deals with a single variable. A bivariate frequency distribution summarizes the data for two variables simultaneously, showing their joint frequencies.

Range is the difference between the largest and the smallest observation in a dataset. It is used to decide the number and size of classes in a frequency distribution.