Class 10 Mathematics – Statistics (Part 1)
Introduction to Statistics & Frequency
Distribution
Introduction
Statistics is the branch of mathematics that deals with the collection, organization,
presentation, analysis, and interpretation of data.
It helps us understand large amounts of information and make informed decisions. Statistics
is widely used in education, business, economics, science, sports, healthcare, and
government.
What is Data?
Data is a collection of facts, figures, or observations gathered for a specific purpose.
Examples
Marks scored by students in a mathematics test.
Heights of students in a class.
Daily temperatures of a city.
Monthly sales of a company.
Types of Data
1. Raw Data
Raw data is the data collected in its original form without any arrangement.
Example
42, 38, 56, 49, 38, 61, 42, 45, 49, 52
,2. Grouped Data
Grouped data is data arranged into class intervals with their corresponding frequencies.
Example
Marks Frequency
0–10 2
10–20 5
20–30 8
30–40 10
Frequency
The frequency of a value is the number of times it occurs in a data set.
Example
Marks: 10, 20, 20, 30, 40, 20
Frequency of 20 = 3
Frequency Distribution Table
A frequency distribution table organizes data into classes and shows how many
observations belong to each class.
Example
Marks Frequency
0–10 3
10–20 5
20–30 7
30–40 6
40–50 4
Total Frequency = 25
,Class Interval
A class interval is the range of values included in a class.
Example
10–20
Lower Limit = 10
Upper Limit = 20
Class Limits
Each class interval has:
Lower Class Limit – the smallest value in the class.
Upper Class Limit – the largest value in the class.
Example
Class Interval: 20–30
Lower Limit = 20
Upper Limit = 30
Class Size (Width)
The class size is calculated as:
Class Size=Upper Limit−Lower Limit\boxed{\text{Class Size} = \text{Upper Limit} -
\text{Lower Limit}}Class Size=Upper Limit−Lower Limit
Example
Class Interval = 30–40
Class Size = 40 − 30 = 10
Class Mark (Midpoint)
, The class mark is the midpoint of a class interval.
Formula
Class Mark=Lower Limit+Upper Limit2\boxed{\text{Class Mark}=\frac{\text{Lower
Limit}+\text{Upper Limit}}{2}}Class Mark=2Lower Limit+Upper Limit
Example
Class Interval = 20–30
20+302=25\frac{20+30}{2}=25220+30=25
Answer: 25
Cumulative Frequency
The cumulative frequency (CF) is the running total of frequencies.
Example
Class Interval Frequency (f) Cumulative Frequency (CF)
0–10 2 2
10–20 5 7
20–30 6 13
30–40 4 17
Important Terms
Term Meaning
Data Collection of observations
Frequency Number of occurrences
Class Interval Group of values
Class Mark Midpoint of a class
Class Size Width of a class
Cumulative Frequency Running total of frequencies
Solved Example 1
Question
Introduction to Statistics & Frequency
Distribution
Introduction
Statistics is the branch of mathematics that deals with the collection, organization,
presentation, analysis, and interpretation of data.
It helps us understand large amounts of information and make informed decisions. Statistics
is widely used in education, business, economics, science, sports, healthcare, and
government.
What is Data?
Data is a collection of facts, figures, or observations gathered for a specific purpose.
Examples
Marks scored by students in a mathematics test.
Heights of students in a class.
Daily temperatures of a city.
Monthly sales of a company.
Types of Data
1. Raw Data
Raw data is the data collected in its original form without any arrangement.
Example
42, 38, 56, 49, 38, 61, 42, 45, 49, 52
,2. Grouped Data
Grouped data is data arranged into class intervals with their corresponding frequencies.
Example
Marks Frequency
0–10 2
10–20 5
20–30 8
30–40 10
Frequency
The frequency of a value is the number of times it occurs in a data set.
Example
Marks: 10, 20, 20, 30, 40, 20
Frequency of 20 = 3
Frequency Distribution Table
A frequency distribution table organizes data into classes and shows how many
observations belong to each class.
Example
Marks Frequency
0–10 3
10–20 5
20–30 7
30–40 6
40–50 4
Total Frequency = 25
,Class Interval
A class interval is the range of values included in a class.
Example
10–20
Lower Limit = 10
Upper Limit = 20
Class Limits
Each class interval has:
Lower Class Limit – the smallest value in the class.
Upper Class Limit – the largest value in the class.
Example
Class Interval: 20–30
Lower Limit = 20
Upper Limit = 30
Class Size (Width)
The class size is calculated as:
Class Size=Upper Limit−Lower Limit\boxed{\text{Class Size} = \text{Upper Limit} -
\text{Lower Limit}}Class Size=Upper Limit−Lower Limit
Example
Class Interval = 30–40
Class Size = 40 − 30 = 10
Class Mark (Midpoint)
, The class mark is the midpoint of a class interval.
Formula
Class Mark=Lower Limit+Upper Limit2\boxed{\text{Class Mark}=\frac{\text{Lower
Limit}+\text{Upper Limit}}{2}}Class Mark=2Lower Limit+Upper Limit
Example
Class Interval = 20–30
20+302=25\frac{20+30}{2}=25220+30=25
Answer: 25
Cumulative Frequency
The cumulative frequency (CF) is the running total of frequencies.
Example
Class Interval Frequency (f) Cumulative Frequency (CF)
0–10 2 2
10–20 5 7
20–30 6 13
30–40 4 17
Important Terms
Term Meaning
Data Collection of observations
Frequency Number of occurrences
Class Interval Group of values
Class Mark Midpoint of a class
Class Size Width of a class
Cumulative Frequency Running total of frequencies
Solved Example 1
Question
