Revision: Statistics and Probability >> Statistics Maths Commerce (English Medium) Class 11 CBSE

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"`

The mode is the value of the observation that occurs most frequently; i.e., the observation with the maximum frequency is called the mode.

The observations which divide the whole set of observations into four equal parts are known as quartiles.

Before finding quartiles, the given data must always be arranged in ascending order of magnitude.

The difference between the largest and smallest values in a data set is called the range.

Range = Largest value − Smallest value

\[ \begin{array}{c} \text{The mean of statistical data} = \dfrac{\text{The sum of all scores}}{\text{Total no. of scores}} = \dfrac{\sum\limits_{i = 1}^{N} x_{i}}{N} \end{array} \]

(Here \[ x_{i} \] is the \[ i^{th} \] score)

Mean is denoted by \[ \overline{X} \] and it represents the average of the given data.

\[ \overline{X} = \frac{\sum\limits_{i = 1}^{N} x_{i}}{N} \]

Inter-quartile range:

The difference between the upper quartile (Q₃) and the lower quartile (Q₁) is called the inter-quartile range.

Inter-quartile range = Q₃ − Q₁

• It is always positive, since Q₃ > Q₁.

Semi-interquartile range:

Half of the inter-quartile range is called the semi-interquartile range.

Semi-interquartile range = `1/2` (Q₃ − Q₁)

Case I: When n is ODD

• Lower Quartile, Q₁ = (n + 1) / 4 th term

• Upper Quartile, Q₃ = 3(n + 1) / 4 th term

Case II: When n is EVEN

• Lower Quartile, Q₁ = n / 4 th term

• Upper Quartile, Q₃ = 3n / 4 th term

• Statistics deals with collecting, organising, analysing, and interpreting data.

• Central tendency gives a single representative value for a data set.

• Mean is the arithmetic average.

• Median is the middle value of ordered data.

• Mode is the most frequently occurring value.

Types of Quartiles

1. Lower Quartile (Q₁)
   The observation lies midway between the lowest value and the median.

2. Middle Quartile (Q₂)
   The median of the data.

3. Upper Quartile (Q₃)
   The observation lies midway between the median and the highest value.