Question:
If the mode of the following classified grouped data is $26$, then find the value of the missing frequency $k$ in the given table:
If the mode of the following classified grouped data is $26$, then find the value of the missing frequency $k$ in the given table:
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The modal class is the class containing the given mode value. Substitute the class parameters directly into the grouped-data mode formula.
Updated On: Jun 12, 2026
- $4$
- $5$
- $6$
- $7$
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The Correct Option is C
Solution and Explanation
Concept:
For grouped data,
$$
\text{Mode}
=
L+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h
$$
where
• $L$ = lower limit of modal class
• $f_1$ = frequency of modal class
• $f_0$ = frequency of preceding class
• $f_2$ = frequency of succeeding class
• $h$ = class width
Step 1: Identify the modal class. Since the mode is $26$, the modal class is $20-30$. Thus, $$ L=20,\quad f_1=9,\quad f_0=k,\quad f_2=7,\quad h=10 $$
Step 2: Apply the mode formula. $$ 26 = 20+\frac{9-k}{2(9)-k-7}\times10 $$ $$ 6 = \frac{10(9-k)}{11-k} $$
Step 3: Solve for $k$. $$ 6(11-k)=10(9-k) $$ $$ 66-6k=90-10k $$ $$ 4k=24 $$ $$ k=6 $$ Therefore, $$ \boxed{k=6} $$
• $L$ = lower limit of modal class
• $f_1$ = frequency of modal class
• $f_0$ = frequency of preceding class
• $f_2$ = frequency of succeeding class
• $h$ = class width
Step 1: Identify the modal class. Since the mode is $26$, the modal class is $20-30$. Thus, $$ L=20,\quad f_1=9,\quad f_0=k,\quad f_2=7,\quad h=10 $$
Step 2: Apply the mode formula. $$ 26 = 20+\frac{9-k}{2(9)-k-7}\times10 $$ $$ 6 = \frac{10(9-k)}{11-k} $$
Step 3: Solve for $k$. $$ 6(11-k)=10(9-k) $$ $$ 66-6k=90-10k $$ $$ 4k=24 $$ $$ k=6 $$ Therefore, $$ \boxed{k=6} $$
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