NCERT Solutions Class 9 Maths Chapter 12 Statistics

Class 9 chapter 12 statistics deals with information about how data can be presented graphically in the form of bar graphs, histogram and frequency polygons. The NCERT class 9 statistics enables the students to know the collection, analysis, interpretation as well as presentation of data information.

By practicing NCERT Solutions for Class 9 Maths statistics solutions, students not only strengthen the understanding of the concept being studied but also enhance their problem solving ability. Every ncert class 9 statistics question is described clearly, giving the students an understanding of the concepts used in statistics. Such an exhaustive practice makes sure that learners are prepared for their exams because statistics is an important subject in mathematics which is essential for higher classes.

1.0Download NCERT Solutions Class 9 Maths Chapter 12 Statistics: Free PDF

In the below table, students can find chapter 12 statistics class 9 pdf which can be downloaded so students can access it anytime and anywhere.

2.0NCERT Solutions Class 9 Maths Chapter 12 Statistics: All Exercises

In addition, answering such questions enables a student to discover his/her areas of weakness and be in a position to attend to them long before their examinations. This way the students get the confidence they need to succeed in exams through enhancing their statistics competence.

3.0What Will Students Learn in Chapter 12: Statistics?

• A guide on how to gather and categorize raw information into valuable information.
• Arithmetic mean, median and mode for describing data.
• Methods including bar graphs, histograms and frequency polygon to display data.
• Frequency and relative frequency, making cumulative frequency tables and cumulative frequency graphs.
• Applying statistical methods to solve real problems that may involve data analysis and/or data interpretation.

4.0NCERT Questions with Solutions for Class 9 Maths Chapter 12 - Detailed Solutions

Exercise : 12.1

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.

2. Which method did you use for finding the mean, and why?

Sol.

We have, $\mathrm{N}=\Sigma {\mathrm{f}}_{\mathrm{i}}=20$ and $\Sigma {\mathrm{f}}_{\mathrm{i}}=162$. Then mean of the data is $\overline{\mathrm{x}}=\frac{1}{\mathrm{N}}\times \Sigma {\mathrm{f}}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{i}}=\frac{1}{20}\times 162=8.1$ Hence, the required mean of the data is 8.1 plants.

We find the mean of the data by direct method because the figures are small.

• Consider the following distribution of daily wages of 50 workers of a factory.

3. Find the mean daily wages of the workers of the factory by using an appropriate method.

Sol.

We have $\sum {\mathrm{f}}_{\mathrm{i}}=50$ and $\sum {\mathrm{f}}_{\mathrm{i}}=27260$ Mean $=\frac{\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}}{\sum {\mathrm{f}}_{\mathrm{i}}}=\frac{27260}{50}$ $=545.2$

4. 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 :

It is given that mean $=18$. From the table, we have $\mathrm{a}=18,\mathrm{N}=44+\mathrm{f}$ and $\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{d}}_{\mathrm{i}}=2\mathrm{f}-40$ Now, mean $=\mathrm{a}+\frac{1}{\mathrm{N}}\times \Sigma {\mathrm{f}}_{\mathrm{i}}{\mathrm{d}}_{\mathrm{i}}$ Then substituting the values as given above, we have $18=18+\frac{1}{44+\mathrm{f}}\times (2\mathrm{f}-40)$ $\Rightarrow 0=\frac{2\mathrm{f}-40}{44+\mathrm{f}}\Rightarrow \mathrm{f}=20$.

5. 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.

Mean $=\frac{\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}}{\sum {\mathrm{f}}_{\mathrm{i}}}=\frac{2277}{30}=75.9$.

6. 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.

7. Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Sol.

$\mathrm{a}=57,\mathrm{h}=3,\mathrm{N}=400$ and $\Sigma {\mathrm{f}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}=25$. By step deviation method, Mean $=\mathrm{a}+\mathrm{h}\times \frac{1}{\mathrm{N}}\times \Sigma {\mathrm{f}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}=57+3\times \frac{1}{400}\times 25$ $=57.19$

• The table below shows the daily expenditure on food of 25 households in a locality.

8. Find the mean daily expenditure on food by a suitable method.

Sol.

Mean $=\frac{\sum {\mathrm{f}}_{{\mathrm{i}}_{\mathrm{i}}}}{\sum {\mathrm{f}}_{\mathrm{i}}}=\frac{5275}{25}=211$

9. To find out the concentration of ${\mathrm{SO}}_2$ 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 :

10. Find the mean concentration of ${\mathrm{SO}}_2$ in the air.

Sol.

Mean $=\frac{\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}}{\sum {\mathrm{f}}_{\mathrm{i}}}=\frac{2.96}{30}=0.0986$

11. 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.

Mean $=\frac{\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}}{\sum {\mathrm{f}}_{\mathrm{i}}}=\frac{499}{40}=12.475$ 12. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Sol.

Mean $=\frac{\sum {\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}}{\sum {\mathrm{f}}_{\mathrm{i}}}=\frac{2430}{35}=69.43$