Our NCERT Solutions Class 9 Maths Chapter 12 Statistics Exercise 12.1 introduces students to the basics of data collection and organization. This exercise focuses on creating frequency tables to represent data clearly and systematically. By working through these problems, students learn how to arrange raw data in a meaningful way, making it easier to analyze and draw conclusions. Understanding these concepts is crucial as statistics plays a vital role in everyday life and higher studies.
The solutions provided for Exercise 12.1 are detailed and easy to follow, helping students avoid confusion and build confidence in handling statistical problems. Each question is solved step by step as per the latest NCERT guidelines, ensuring students grasp both the methods and logic behind each answer. These solutions are an excellent tool for thorough practice and effective exam preparation.
Gain access to free and well-structured and accurate NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.1. These solutions will help clarify concepts of data collection and data representation. You will find answers for all questions in the textbook along with step-by-step answers.
Here is a quick overview and access to solutions for all exercises from Chapter 12, Surface Area and Volume.
1. A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.
Which method did you use for finding the mean, and why?
Sol.
To find the mean, we can create the following table:
We have, N = Σfᵢ = 20 and Σfᵢxᵢ = 162.
Then the mean of the data is x̄ = (1/N) × Σfᵢxᵢ = (1/20) × 162 = 8.1.
Hence, the required mean of the data is 8.1 plants.
We find the mean of the data by the direct method because the figures (frequencies and class marks) are small, making calculations straightforward.
2. Consider the following distribution of daily wages of 50 workers of a factory.
Find the mean daily wages of the workers of the factory by using an appropriate method.
Sol.
To find the mean, we can prepare the following table:
We have Σfᵢ = 50 and Σfᵢxᵢ = 27260.
Mean = Σfᵢxᵢ / Σfᵢ = 27260 / 50 = 545.2 Rs.
3. The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs. 18. Find the missing frequency f.
Sol. We may prepare the table as given below, using the Assumed Mean Method since we have a missing frequency and a given mean. Let the assumed mean (a) be 18.
It is given that mean = 18.
From the table, we have a = 18, N = 44 + f, and Σfᵢdᵢ = 2f − 40.
Now, Mean = a + (1/N) × Σfᵢdᵢ
Substituting the values as given above, we have:
18 = 18 + (1/(44+f)) × (2f−40)
0 = (2f−40) / (44+f)
Since 44+f cannot be zero (as frequency is always positive), the numerator must be zero:
2f − 40 = 0
2f = 40
f = 20.
4. Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.
Sol.
To find the mean, we can prepare the following table using the Direct Method:
Mean = Σfᵢxᵢ / Σfᵢ = 2277 / 30 = 75.9.
5. In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.
6. Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
Sol.
First, notice that the class intervals are inclusive. To make them continuous (exclusive), we adjust the boundaries by 0.5. For example, 50-52 becomes 49.5-52.5.
Then we choose the Step Deviation Method as the class marks are relatively large, simplifying calculations. Let assumed mean (a) = 57 and class size (h) = 3.
We have a = 57, h = 3, N = 400, and Σfᵢuᵢ = 25.
By the Step Deviation Method:
Mean = a + h × (1/N) × Σfᵢuᵢ
= 57 + 3 × (1/400) × 25
= 57 + (75/400)
= 57 + 0.1875
= 57.1875 (or approximately 57.19)
7. The table below shows the daily expenditure on food of 25 households in a locality.
Find the mean daily expenditure on food by a suitable method.
Sol.
To find the mean, we can use the Direct Method:
Mean = Σfᵢxᵢ / Σfᵢ = 5275 / 25 = 211 Rs.
8. To find out the concentration of SO₂ in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:
Find the mean concentration of SO₂ in the air.
Sol.
To find the mean, we can use the Direct Method:
Mean = Σfᵢxᵢ / Σfᵢ = 2.96 / 30 = 0.0986 ppm (approximately).
9. A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.
Sol.
To find the mean, we can use the Direct Method:
Mean = Σfᵢxᵢ / Σfᵢ = 499 / 40 = 12.475 days.
10. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Sol.
To find the mean, we can use the Direct Method:
Mean = Σfᵢxᵢ / Σfᵢ = 2430 / 35 = 69.43% (approximately).
(Session 2025 - 26)