NCERT Solutions for Class 10 Maths Chapter 13 Statistics

CBSE Maths Chapter 13 Statistics plays an important role in various fields of science.  This chapter covers the key concepts of statistics for the students, including mean, median, mode, and cumulative frequency distribution.

In this blog, ALLEN provides detailed NCERT Solutions for Class 10 Maths Chapter 13. The solutions help students acquire proper knowledge of these concepts and foster problem-solving skills.

1.0Download NCERT Solutions Class 10 Chapter 13 Statistics : Free PDF 

Students can download the NCERT Solutions for Class 10 Maths Chapter 13 Statistics by ALLEN here in PDF format: With these solutions, students will be more adequately prepared for their exams, and they will gain greater consolidation of the concepts learned in Chapter 13: Statistics

2.0NCERT Exercise-wise Solutions for Class 10 Maths Chapter 13 Statistics

3.0Important Topics of Class 10 Maths Chapter 13 Statistics

Chapter 13: Statistics in Class 10 Math focuses on the collection, organization, and analysis of data. It covers key concepts like mean, median, mode, cumulative frequency, histograms, and ogives. The chapter teaches how to interpret data through tables and graphs, enabling the analysis of real-life situations. By understanding and applying these statistical tools, you can make sense of data distributions and make informed decisions based on numerical information.

1. Mean, Median, and Mode
2. Cumulative Frequency 
3. Construction of Cumulative Frequency Tables 
4. Histogram
5. Ogive (Cumulative Frequency Curve)
6. Measures of Central Tendency

4.0General Outline for Class 10 Maths Chapter 13 Statistics

Introduction to Statistics

Types of Data:

• Raw Data: Unprocessed data collected from various sources.
• Grouped Data: Data presented in intervals or classes (frequency distribution).
• Continuous and Discrete Data: Discuss the differences between continuous (measured) and discrete (counted) data.

Key Concepts and Formulas

1. Mean:

• Mean is the average of all data points.
• Formula: $\text{Mean}=\frac{\sum f\cdot x}{\sum f}$, where f is the frequency and x is the data point (for grouped data).

2. Median:

• Formula (for grouped data): $\text{Median}=L+\left(\frac{\frac{N}{2}-F}{f}\right)\times h$, where L is the lower class boundary, N is the total number of observations, F is the cumulative frequency before the median class, f is the frequency of the median class, and hh is the class width.
• The median is the middle value that divides the data set into two equal halves.

3. Mode:

• Formula (for grouped data): $\text{Mode}=L+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$, where $f_1$ is the frequency of the modal class, $f_0$ and $f_2$ are the frequencies of the classes before and after the modal class, respectively, and L is the lower class boundary of the modal class.

4. Range:

• Formula: $\text{Range}=\text{Highest value}-\text{Lowest value}$
• Range gives a measure of the spread of the data.

5. Cumulative Frequency: Cumulative frequency is the sum of the frequencies of all classes up to the current class.

• It is used in the construction of cumulative frequency distributions and in finding the median and percentiles.

6. Graphical Representations:

• Histogram: A bar graph representing frequency distributions for continuous data.
• Frequency Polygon: A line graph formed by joining the midpoints of the tops of the bars of a histogram.

5.0Sample NCERT Solutions for Class 10 Maths Chapter 13 Statistics

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.

We have, N=Σfi​=20 and Σfi​=162.
Then mean of the data is
x= N1​×Σfi​Xi​=201​×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.

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.

We have ∑fi​=50 and ∑fi​=27260
Mean =∑fi​∑fi​xi​​=5027260​
=545.2

3. The following table shows the ages of the patients admitted in a hospital during a year :

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Sol.

From the given data, we have the modal class 35-45.
{∵ It has largest frequency among the given classes of the data}
So, ℓ=35,fm​=23,f1​=21,f2​=14
and h=10

Mode =ℓ+{2fm​−f1​−f2​fm​−f1​​}×h
=35+{46−21−1423−21​}×10=35+1120​
=36.8 years
Now, let us find the mean of the data :

a=30, h=10, N=80 and ∑fi​ui​=43
Mean =a+h× N1​×Σfi​ui​=30+10×801​×43
=30+5.37=35.37 years
Thus, mode =36.8 years and mean =35.37 years.
So, we conclude that the maximum number of patients admitted in the hospital are of the age 36.8 years (approx), whereas on an average the age of a patient admitted to the hospital is 35.37 years.

4. The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Sol.

(i)

n=68 gives 2N​=34
So, we have the median class (125-145)
ℓ=125, N=68,f=20,cf=22, h=20
Median =ℓ+{f2N​−cf​}×h
=125+{2034−22​}×20=137 units.
(ii) Modal class is (125 - 145) having maximum frequency f1​=20,f0​=13,f2​=14, ℓ=125 and h=20
Mode =ℓ+{2f1​−f0​−f2​f1​−f0​​}×h=125+{40−13−1420−13​}×20=125+
137×20​
=125+13140​=125+10.76=135.76 units
(iii)

N=68,a=135, h=20 and Σfi​ui​=7
By step-deviation method.
Mean =a+h× N1​×Σfi​ui​
=135+20×681​×7
=135+1735​=135+2.05
=137.05 units

5. The following distribution gives the daily income of 50 workers of a factory.

Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.

Sol.

N=50 gives 2N​=25
On the graph, we will plot the points (120,12),(140,26),(160,34),(180,40), (200,50).

6.0Benefits of Introduction to Statistics 

The Statistics chapter in Class 10 Maths offers several key benefits:

1. Data Analysis Skills: It teaches how to collect, organize, and interpret data, which is useful for making informed decisions in various fields like business, economics, and social sciences.
2. Real-Life Applications: Statistics is widely used in surveys, polls, and research to analyze trends, patterns, and probabilities.
3. Problem-Solving Abilities: Students develop the ability to calculate measures like mean, median, mode, and understand data distribution.
4. Foundation for Further Studies: It provides a solid base for advanced studies in statistics, probability, and data science.

7.0Facts Related to NCERT Class 10 Maths Chapter 13 Statistics

Let's have an overview of the main things you should remember from the given CBSE Solutions for Class 10 Maths Chapter 13 to score well in your exam:

• Statistics is the art of collecting, analyzing, and presenting data.
• Statistics play a crucial role in planning for businesses, economics, governments, and individuals.
• The arithmetic mean is the middle value determined by dividing the sum of all observations by the number of observations.
• The median is the middle value of a distribution that divides it into two equal parts.
• The mode is the value of the variable with the highest frequency in the distribution.
• The relationship between the three central measures of tendency is given by: Mode = 3 Median - 2 Mean.
• The median is the middlemost value of observations in a set arranged in ascending or descending order.
• The mode is the most frequent value in a given data set.