Revision: Statistics Algebra SSC (English Medium) 9th Standard Maharashtra State Board

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.

Double bar graph: A double bar graph is a graphical display of information using two bars beside each other at various heights.

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

• 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)

Frequency:

The number of times a particular observation occurs.

Frequency Distribution:

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

The difference between the highest and lowest observations.

Range = Highest value − Lowest value

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

Data is a collection of facts, information, or observations, usually in numerical form.

• Example: The heights of all the children in your class.

• 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.

Frequency Distribution Table: When the number of observations in an experiment is large then we can convert it into the tabular form which is called a Frequency Distribution Table.

Ungrouped Frequency Distribution Table: When the frequency of each class interval is not arranged or organized in any manner.

Grouped Frequency Distribution Table: The frequencies of the corresponding class intervals are organised or arranged in a particular manner, either ascending or descending. 

Inclusive or discontinuous Frequency Distribution: A frequency distribution in which the upper limit of one class differs from the lower limit of the succeeding class is called an Inclusive or discontinuous Frequency Distribution.

Exclusive or continuous Frequency Distribution: A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an exclusive or continuous Frequency Distribution.

The cumulative frequency of a class interval is the sum of the frequencies of all the classes up to this class interval.

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 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.

\[\mathbf{Mean}=\frac{\left(x_1+x_2+x_3+\ldots+x_n\right)}{n}=\frac{\Sigma x_i}{n}\] 

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.

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

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

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

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