
How to derive the mode formula for grouped data?
Answer
494.7k+ views
Hint: To solve this question, we will first make 3 bar graphs of frequencies Mode is the value of the highest bar as that is of the maximum frequency. Finally, we will calculate the midpoint of the largest bar to get the value of the mode formula.
Complete step-by-step answer:
Let us first define the mode for grouped data. The mode of a list of data values is simply the most common values (or the values if any). When the data are grouped as in a histogram, we will normally talk only about the modal class (the class, or group with the greatest frequency) because we don’t know the individual values. The derivation of the mode formula is given by using the bar graph.
Let the frequency of the modal class be The frequency of the class first after the modal class is From the above figure, we see that, triangle AEB is similar to triangle DEC.
The relative side ratio is also equal.
And BE is nothing but and
Again we have from the figure.
Clearly, and
Therefore, we have,
We know that so we can write
Let, FE be x.
Therefore, the mode can be obtained by adding this value of x to
Substituting the value of x as obtained from above, we get,
Hence, the mode formula is determined.
Note: We have used the bar graph to determine the mode formula. So, is considered a point after the first bar and the midpoint of the highest bar is the mode. The highest bar is in the middle. So, we have assumed x = midpoint of the largest bar and hence calculate to get the mode value.
Complete step-by-step answer:
Let us first define the mode for grouped data. The mode of a list of data values is simply the most common values (or the values if any). When the data are grouped as in a histogram, we will normally talk only about the modal class (the class, or group with the greatest frequency) because we don’t know the individual values. The derivation of the mode formula is given by using the bar graph.

Let the frequency of the modal class be
The relative side ratio is also equal.
And BE is nothing but
Again we have
Clearly,
Therefore, we have,
We know that
Let, FE be x.
Therefore, the mode can be obtained by adding this value of x to
Substituting the value of x as obtained from above, we get,
Hence, the mode formula is determined.
Note: We have used the bar graph to determine the mode formula. So,
Latest Vedantu courses for you
Grade 8 | ICSE | SCHOOL | English
Vedantu ICSE 8 Pro Courses(2025-26)
School Full course for ICSE students
₹35,200 per year
EMI starts from ₹2,933.34 per month
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

State and prove Bernoullis theorem class 11 physics CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells
