NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 (Statistics): Mode of Grouped Data

NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 teaches you how to find the mode of grouped data: the value that occurs most often when the data is given as class intervals. The six questions use real data, such as the ages of hospital patients, the lifetimes of electrical components, the monthly expenditure of families, the number of students per teacher, the runs scored by batsmen, and the number of cars on a road. Three of them (Questions 1, 3 and 4) also ask for the mean, so that you can compare the two measures. Below, you get the answers to NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 to check your work, the method, a worked example, practice questions and the facts that the board exam asks.

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What You Will Learn From Exercise 13.2

By the end of NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2, you will know:

• How to find the modal class, the class interval with the highest frequency.
• How to use the mode formula to estimate the mode inside the modal class.
• How to find the mean of grouped data by the direct method and by the step-deviation method (Questions 1, 3 and 4).
• How to compare the mean and the mode and write one line of interpretation.
• When the mode is a better measure than the mean.

Key Terms You Need for the Mode of Grouped Data

NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 at a Glance

A small difference in the last digit of the answers of NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 (for example 35.37 or 35.38, and 4608.69 or 4608.7) comes from rounding. Keep two or three decimals, and round only at the end.

NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2: Mode of Grouped Data Formula

Every question of NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 uses one formula. In ungrouped data, the mode is the value that occurs most often. In grouped data, we cannot see the exact value, so we first find the modal class, and then we estimate the mode inside it:

$$\text{Mode} = l + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h$$

How to find the mode of grouped data in 4 steps:

1. Find the class with the highest frequency. This is the modal class.
2. Write $l$, $h$, $f_1$, $f_0$ and $f_2$ from the table.
3. Put the values in the formula, and simplify the bracket first.
4. Check that the mode lies inside the modal class. If it does not, an error has crept in.

Syllabus note: the CBSE Class 10 Maths syllabus for 2026-27 (Statistics) asks for the mean, median and mode of grouped data, and it says that the bimodal situation is to be avoided. So the data in Class 10 Maths Chapter 13 Exercise 13.2 has one modal class.

Worked Example for NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2

Before you start NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2, try this eSaral worked example. The marks of 40 students are given below. Find the mode.

The highest frequency is 15, so the modal class is 20–30. Here $l = 20$, $f_1 = 15$, $f_0 = 8$, $f_2 = 7$ and $h = 10$.

$$\text{Mode} = 20 + \frac{15 - 8}{2(15) - 8 - 7} \times 10 = 20 + \frac{7}{15} \times 10 \approx 20 + 4.67 = 24.67$$

The mode is about 24.67 marks, and it lies inside the modal class 20–30, as it should.

Which Method to Use for the Mean in NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2

Three questions of NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 also ask for the mean. These checkpoints show which method each question uses, so that you can compare your own values:

Real-Life Uses of the Mode

The mode is used in daily life, and NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 shows some of these uses:

• Shops and manufacturers use the mode to decide which shirt or shoe size to stock the most.
• Hospitals can find the most common age group of patients (Question 1).
• Road planners look at the most common number of vehicles in a period of time (Question 6).
• Television channels find the most popular programme.
• Schools and governments find the most common student-teacher ratio (Question 4).

How to Write the Interpretation in Questions 1, 3 and 4

Questions 1, 3 and 4 of NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 ask for both the mean and the mode, and CBSE expects one line that compares them:

• If the two are close (Question 1: mode 36.8 and mean about 35.4), say that the data is spread fairly evenly around the middle.
• If the mean is much higher than the mode (Question 3: mode about ₹1848 and mean ₹2662.5), say that a few high values pull the average up, while most families spend near the modal value.
• Always say it in the context of the question, for example “most patients are about 36.8 years old, and the average age is about 35.4 years”.

Practice Questions for NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2

Try these two extra questions after you finish NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2.

Practice 1. The daily wages of 50 workers are: ₹100–150: 4 workers, ₹150–200: 10, ₹200–250: 18, ₹250–300: 12, ₹300–350: 6. Find the modal daily wage.

Practice 2. The number of books that 50 students borrowed in a month: 0–5: 3 students, 5–10: 7, 10–15: 12, 15–20: 20, 20–25: 8. Find the mode.

Answers: Practice 1: the modal class is 200–250, so the mode $= 200 + \dfrac{18 - 10}{36 - 10 - 12} \times 50 \approx$ ₹228.57. Practice 2: the modal class is 15–20, so the mode $= 15 + \dfrac{20 - 12}{40 - 12 - 8} \times 5 =$ 17 books.

Tips for Solving NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2

1. Make a small table first (this is eSaral’s first tip for every Statistics question). Write the class, the frequency and the class mark (for the mean) in one table.
2. Mark the modal class with a circle, and write $l$, $h$, $f_1$, $f_0$ and $f_2$ next to it before you substitute.
3. Do not mix up $f_0$ and $f_2$. $f_0$ is the class before the modal class, and $f_2$ is the class after it.
4. Remember $h$. The fraction is multiplied by the class size.
5. Write the units (years, hours, ₹, runs, cars) and one line of interpretation.
6. Practise the other two exercises of the chapter: Exercise 13.1 for the mean, and Exercise 13.3 for the median.

More from the chapter on eSaral: Exercise 13.1 (mean of grouped data), Exercise 13.3 (median of grouped data), all of Chapter 13 Statistics and the NCERT Solutions for Class 10 Maths page.