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

Frequency:

The number of times a particular observation occurs.

Frequency Distribution:

A tabular arrangement of data showing the frequency of each observation or class.

Statistics is the area of study dealing with the collection, presentation, and analysis of data as well as drawing meaningful conclusions from the data.

A collection of given facts or figures, usually expressed in numerical form.

Each group into which raw data is divided is called a class interval.

The two values that bound a class interval.

• Lower limit: Smallest value of the class

• Upper limit: Largest value of the class

The difference between the highest and lowest observations.

Range = Highest value − Lowest value

• Inclusive form: Both lower and upper limits are included in the class.
  (Example: 1–10, 11–20)

• Exclusive form: Lower limit is included, but upper limit is excluded.
  (Example: 0–10, 10–20)

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

\[\text{Adjustment Factor}=\frac{1}{2}\text{(Lower limit of next class - Upper limit of previous class)}\]

\[\text{Frequency density}=\frac{\mathrm{Frequency}}{\text{Class width}}\]

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

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.