A systematic record of facts or different values of a quantity is called data. Data is of two types – Primary data and Secondary data. The data collected by a researcher with a specific purpose in mind is called primary data. The data gathered from a source where it already exists is called secondary data.
The difference between the highest and lowest values in the given data is called the range of the given data. The number of times a value occurs in the given data is called the 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 the given data is called an ungrouped frequency distribution table. A table that shows the frequency of groups of values in the given data is called a grouped frequency distribution table.
The groupings used to group the values in given data are called classes or class-intervals. The number of values that 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 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 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.
The mean of a given set of values is equal to the sum of all the values divided by the total number of values.
The median is that value of the given number of observations, which divides it into exactly two parts.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 = [ (n+1)/2]th value, where n = number of given values.
If the number of given values is even, Median = Mean of (n/2)th and (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 the mode of the given data or an observation with maximum frequency is known as mode.
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.
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