Collection and Representation of Data
* A systematic record of facts or different values of a quantity is called data.
* The data collected by a researcher with a specific purpose in mind is called primary data.
* The data gathered from a source where is already exists is called secondary data.
* The deference between the highest and lowest value in the given data is called the range of given data.
* The number of times a value occurs in the given data is called frequency of that value.
* A table that shows the frequency of different values in the given data is called a frequency distribution table.
* A frequency distribution table that shows the frequency of each individual value in given data is called an ungrouped frequency distribution table.
* A table that shows the frequency of a group of values in the given data is called a grouped frequency distribution table.
* The grouping used to group the values in given data is called classes or classintervals.
* The number of values each class contains is called the class size or class width.
* The lower value in a class is called the lower class limit.
* The higher value in a class is called the upper class limit.
Graphical Representation of Data
* Graphical representation of data helps in faster and easier interpretation of data.
* A bar graph uses bars or rectangles of the same width but different heights to represent different values of data.
In a bar graph:
* The bars have equal gaps between them.
* The width of the bars does not matter.
* The height of the bars represents the different values of the variable.
In a histogram:
* The bars do not have gaps between them.
* The width of the bars is proportional to the class intervals of the data.
* The height of the bars represents the different values of the variable.
* The area of each rectangle is proportional to its corresponding frequency.
* The area of a histogram is equal to the area enclosed by its corresponding frequency polygon.
Measures of Central Tendencies
* The mean of the given set of values is equal to the sum of all the values divided by the total number of values.
* The value that lies in the very centre of a given set of values arranged in ascending or descending order is called the median of the given data.
* If the number of given values is odd, Median = \frac{ n + 1}{2} th values, where n = number of given values.
* If the number of given values is even, Median = Mean of \frac{ n}{2} th and ( \frac{ n}{2} + 1)th values where n = number of given values.
* The value that occurs the most number of times in a given set of values is called mode of the given data.
* Mean, Median and Mode together are called the measures of central tendencies of data.
* The central tendencies of data depend on distribution of values and must be considered with other information for effective interpretation of data.