Question

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 1

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.