Definitions [3]
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.
Answer the following question in about 30 words:
Define the mean.
The mean is the value that is derived by summing all the values and dividing it by the number of observations.
`bar"x" = "Sum of observations"/"No. of observations"`
Formulae [1]
\[ \begin{array}{c} \text{The mean of statistical data} = \dfrac{\text{The sum of all scores}}{\text{Total no. of scores}} = \dfrac{\sum\limits_{i = 1}^{N} x_{i}}{N} \end{array} \]
(Here \[ x_{i} \] is the \[ i^{th} \] score)
Mean is denoted by \[ \overline{X} \] and it represents the average of the given data.
\[ \overline{X} = \frac{\sum\limits_{i = 1}^{N} x_{i}}{N} \]
Key Points
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Statistics deals with collecting, organising, analysing, and interpreting data.
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Central tendency gives a single representative value for a data set.
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Mean is the arithmetic average.
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Median is the middle value of ordered data.
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Mode is the most frequently occurring value.
