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.
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
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.
Types of Data:
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×ΣfiXi=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∑fixi=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−f2fm−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 ∑fiui=43
Mean =a+h× N1×Σfiui=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−f2f1−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 Σfiui=7
By step-deviation method.
Mean =a+h× N1×Σfiui
=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).
The Statistics chapter in Class 10 Maths offers several key benefits:
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:
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