
For a continuous series, the mode is computed by the formula
A. \[l + \dfrac{{{f_m} - {f_{m - 1}}}}{{{f_m} - {f_{m - 1}} - {f_{m + 1}}}}\] or \[l + \dfrac{{{f_m} - {f_1}}}{{{f_m} - {f_1} - {f_2}}}\]
B. \[l + \dfrac{{{f_m} - {f_{m - 1}}}}{{2{f_m} - {f_{m - 1}} - {f_{m + 1}}}} \times c\] or \[l + \dfrac{{{f_m} - {f_1}}}{{2{f_m} - {f_1} - {f_2}}} \times i\]
C. \[l + \dfrac{{2{f_m} - {f_{m - 1}}}}{{{f_m} - {f_{m - 1}} - {f_{m + 1}}}}\] or \[l + \dfrac{{2{f_m} - {f_1}}}{{{f_m} - {f_1} - {f_2}}}\]
D. \[l + \dfrac{{{f_{m - 1}}}}{{{f_m} - {f_{m - 1}} - {f_{m + 1}}}} \times c\] or \[l + \dfrac{{{f_1}}}{{{f_m} - {f_1} - {f_2}}}\]
Answer
162.3k+ views
Hint: There are two types of series in statistics. One is a discrete series and the other is a continuous series. Discrete series is formed by ungrouped data and continuous series is formed by grouped data. In both the series, all the class intervals along with their corresponding frequencies are listed in a table. Frequency means number of repetitions of an observation given in the data. Mode is a measurement of the central tendency of the data. Mode is a value which appears maximum times in the series. There is a formula for finding the mode of the given data in case of a continuous series.
Complete step-by-step solution:
There is a particular procedure for finding the mode of a continuous series.
First, you have to make a table representing the given values in the form of a class, frequencies \[\left( {{f_i}} \right)\], cumulative frequencies obtained by addition of the corresponding frequency and its previous frequencies. After that you have to find the modal class. The class corresponding to the maximum frequency is the modal class.
Let \[l = \]lower limit of the modal class
\[c\] or \[i = \]size of the class interval
\[{f_m} = \]frequency of the modal class
\[{f_1}\] or \[{f_{m - 1}} = \]frequency of the class preceding the modal class
\[{f_2}\] or \[{f_{m + 1}} = \]frequency of the class succeeding the modal class
The formula for computation of the mode is given by
\[Mode = l + \dfrac{{{f_m} - {f_{m - 1}}}}{{2{f_m} - {f_{m - 1}} - {f_{m + 1}}}} \times c\] or \[l + \dfrac{{{f_m} - {f_1}}}{{2{f_m} - {f_1} - {f_2}}} \times i\]
After finding all the values of the symbols from the table and putting in the formula, the mode can be obtained.
Hence option B is the correct answer.
Note: The formula is not useful for discrete series. It is necessary for a continuous series. Be careful about placing the symbols. Many students can’t remember the actual place of the symbols and obtain a wrong mode.
Complete step-by-step solution:
There is a particular procedure for finding the mode of a continuous series.
First, you have to make a table representing the given values in the form of a class, frequencies \[\left( {{f_i}} \right)\], cumulative frequencies obtained by addition of the corresponding frequency and its previous frequencies. After that you have to find the modal class. The class corresponding to the maximum frequency is the modal class.
Let \[l = \]lower limit of the modal class
\[c\] or \[i = \]size of the class interval
\[{f_m} = \]frequency of the modal class
\[{f_1}\] or \[{f_{m - 1}} = \]frequency of the class preceding the modal class
\[{f_2}\] or \[{f_{m + 1}} = \]frequency of the class succeeding the modal class
The formula for computation of the mode is given by
\[Mode = l + \dfrac{{{f_m} - {f_{m - 1}}}}{{2{f_m} - {f_{m - 1}} - {f_{m + 1}}}} \times c\] or \[l + \dfrac{{{f_m} - {f_1}}}{{2{f_m} - {f_1} - {f_2}}} \times i\]
After finding all the values of the symbols from the table and putting in the formula, the mode can be obtained.
Hence option B is the correct answer.
Note: The formula is not useful for discrete series. It is necessary for a continuous series. Be careful about placing the symbols. Many students can’t remember the actual place of the symbols and obtain a wrong mode.
Recently Updated Pages
If there are 25 railway stations on a railway line class 11 maths JEE_Main

Minimum area of the circle which touches the parabolas class 11 maths JEE_Main

Which of the following is the empty set A x x is a class 11 maths JEE_Main

The number of ways of selecting two squares on chessboard class 11 maths JEE_Main

Find the points common to the hyperbola 25x2 9y2 2-class-11-maths-JEE_Main

A box contains 6 balls which may be all of different class 11 maths JEE_Main

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Degree of Dissociation and Its Formula With Solved Example for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

JoSAA JEE Main & Advanced 2025 Counselling: Registration Dates, Documents, Fees, Seat Allotment & Cut‑offs

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

NCERT Solutions for Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations

NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations

NCERT Solutions for Class 11 Maths In Hindi Chapter 1 Sets

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More
