মোহাম্মদ সায়েম হোসাইন
সহকারী শিক্ষক
২৯ জুন, ২০২৪ ০৯:০৩ অপরাহ্ণ
Chapter -17 Statistics Class : 9 | Median | Statistics | NCTB | English Version
ধরন: সাধারণ শিক্ষা
শ্রেণি: নবম
বিষয়: গণিত
অধ্যায়: সপ্তদশ অধ্যায়
Chapter -17
Statistics
Class : 9
Important definitions and formulae :
Cumulative Frequency : Sum of the frequency of a class with the frequency of previous class is
called cumulative frequency of that class .
Variable: The numerical information in data of statistics is known as variable . There are two types of variables , such as discrete variable and indiscrete variable .
Discrete Variable : The variables in which values are only integers are called discrete variable.
For example, the variables of the data used for population are discrete variables .
Indiscrete Variable : The variables in which values are any real numbers are called indiscrete
variable. For example , the variables of the data used for temperature, age, height, weight
are discrete variables .
Frequency Polygon : It is one kind of graphical representations of statistics which is drawn by joining consecutive midpoints of each class interval .
Cumulative Frequency Diagram or Ogive curve : It is one kind of graphical representations of statistics which is drawn by joining consecutive cumulative frequencies of a table .
Discrete or Discontinuous class interval : In a frequency distribution table , if higher limit of a class and lower limit of next class are consecutive numbers or integers (not same ), then the class interval of that frequency distribution table is called Discrete or Discontinuous class interval .
Such as, (25-29) and (30-34) are discrete class interval .
Indiscrete or continuous class interval : In a frequency distribution table , if higher limit of a class and lower limit of next class are same number , then the class interval of that frequency distribution table is called indiscrete or continuous class interval.
Such as, (24.5 -29.5) and (29.5-34.5) are indiscrete class interval .
Central Tendency : If the unorganized data of statistics are arranged according to the value , the data cluster round near any central value .Moreover abundance of data is observed in a single class when these data are presented in some frequency distribution table .This tendency of data to cluster around central value is known as central tendency .
The measurement of central tendency is of three types . These are arithmetic mean , median and mode .
Arithmetic Mean : If the sum of data is divided by the number of data , then it is called arithmetic mean .
Therefore , Arithmetic mean = ; n = total frequency , = frequency
and = class mid value
There is another formula to find out arithmetic mean of classified data in shot-cut method .
Arithmetic mean , = a + X h
Here , a = approximated mean from the mid values
= class frequency of ith class
= step deviation of ith class =
n = total frequency
h = class interval
= Summation
Median :The value of the data which divides the data when arranged in ascending order into two equal parts are median of the data .
Formula : When n is odd number , median = th term ; n = total number of data
When n is even number , median = {th term + (+1) th term }
Median of classified data : If the number of classified data is n , the value of th term of classified data is median.
Therefore, Median = L + ( - ) X ;
Where , L = lower limit of median class, =Cumulative frequency of previous class of
median class , = frequency of median class , h = class interval
Mode: The number which appears maximum times in a data is the mode of the data . In a data , there may ne one or more mode . If there is no repetition of a number in a data , then the data have no mode .
Mode of classified data : If data is classified in a frequency distribution table , then the formula to determine mode is given below .
Mode class is identified by observing maximum number as frequency.
Mode = L + X h ;
Where , L = lower limit of mode class , h = class interval ,
=Frequency of mode class - frequency of previous class
=Frequency of mode class - frequency of next class
Evaluation
(All kinds of sample questions are given below using the following data or stem )
Marks obtained in Mathematics of 30 students are given below :
70 68 95 65 78 82 86 81 85 90 97 86 78 71 77
92 90 83 69 87 80 82 95 97 75 77 79 80 91 73
a) Form a frequency distribution table using above data .
b) Draw the histogram of the frequency distribution table .
c) Draw a frequency polygon of the frequency distribution table .
d) Draw the ogive curve of the table .
e) Determine arithmetic mean of the table using short-cut method .
f) Determine median and mode of the table.