Definitions [7]
Data is a collection of facts, information, or observations, usually in numerical form.
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Example: The heights of all the children in your class.
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Example: The marks obtained by 20 students in a math test.
Raw Data is the information that you have just collected, and it is completely unsorted or unarranged. It's like a messy pile of clothes!
Example (Marks): Imagine a teacher writes the test marks of 15 students on the board:
72, 77, 67, 74, 82, 80, 66, 90, 78, 57, 56, 54, 74, 72, 92
This long list is Raw Data. It's hard to quickly tell who scored the highest or lowest mark.
Average: Average is a number that represents or shows the central tendency of a group of observations or data.
The arithmetic mean (or, simply, mean) of a set of numbers is obtained by dividing the sum of the numbers in the set by the number of numbers.
\[\mathbf{Mean}=\frac{\left(x_1+x_2+x_3+\ldots+x_n\right)}{n}=\frac{\Sigma x_i}{n}\]
The mode is the value of the observation that occurs most frequently; i.e., the observation with the maximum frequency is called the mode.
Median is the value of the middle-most observation(s). The median is a measure of central tendency which gives the value of the middle-most observation in the data.
A Pictograph is a chart that uses pictures or symbols to represent data. Each picture stands for a specific number of items, making the data easy to understand at a glance.
Formulae [3]
Average = `"sum of the values of all the observations"/"total number of observations"`
If the number of data points (n) is odd, the median is,
Median = `((n+1)/2)^(th)` term
If n is even, the median is the average of the values at positions
Median = Average of `(n/2)^(th)` and `(n/2+1)^(th)` values
