Exercise 14.4 Page: 293
1. The following distribution gives the daily income of 50 workers if a factory. Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.
| Daily income in Rupees | 100-120 | 120-140 | 140-160 | 160-180 | 180-200 |
| Number of workers | 12 | 14 | 8 | 6 | 10 |
Solution
Convert the given distribution table to a less than type cumulative frequency distribution, and we get
| Daily income | Frequency | Cumulative Frequency |
| Less than 120 | 12 | 12 |
| Less than 140 | 14 | 26 |
| Less than 160 | 8 | 34 |
| Less than 180 | 6 | 40 |
| Less than 200 | 10 | 50 |
From the table plot the points corresponding to the ordered pairs such as (120, 12), (140, 26), (160, 34), (180, 40) and (200, 50) on graph paper and the plotted points are joined to get a smooth curve and the obtained curve is known as less than type ogive curve
2.During the medical check-up of 35 students of a class, their weights were recorded as follows:
| Weight in kg | Number of students |
| Less than 38 | 0 |
| Less than 40 | 3 |
| Less than 42 | 5 |
| Less than 44 | 9 |
| Less than 46 | 14 |
| Less than 48 | 28 |
| Less than 50 | 32 |
| Less than 52 | 35 |
Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.
Solution:
From the given data, to represent the table in the form of graph, choose the upper limits of the class intervals are in x-axis and frequencies on y-axis by choosing the convenient scale. Now plot the points corresponding to the ordered pairs given by (38, 0), (40, 3), (42, 5), (44, 9),(46, 14), (48, 28), (50, 32) and (52, 35) on a graph paper an join them to get a smooth curve. The curve obtained is known as less than type ogive.
Locate the point 17.5 on the y-axis and draw a line parallel to the x-axis cutting the curve at a point. From the point, draw a perpendicular line to the x-axis. The intersection point perpendicular to x-axis is the median of the given data. Now, to find the mode by making a table.
| Class interval | Number of students(Frequency) | Cumulative Frequency |
| Less than 38 | 0 | 0 |
| Less than 40 | 3-0=3 | 3 |
| Less than 42 | 5-3=2 | 5 |
| Less than 44 | 9-5=4 | 9 |
| Less than 46 | 14-9=5 | 14 |
| Less than 48 | 28-14=14 | 28 |
| Less than 50 | 32-28=4 | 32 |
| Less than 52 | 35-22=3 | 35 |
The class 46 – 48 has the maximum frequency, therefore, this is modal class
Here, l = 46, h = 2, f1= 14, f0= 5 and f2 = 4
The mode formula is given as:
Now, Mode =
= 46 + 0.95 = 46.95
Thus, mode is verified.
3. The following tables gives production yield per hectare of wheat of 100 farms of a village.
| Production Yield | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 | 75-80 |
| Number of farms | 2 | 8 | 12 | 24 | 38 | 16 |
Change the distribution to a more than type distribution and draw its ogive.
Solution:
Converting the given distribution to a more than type distribution, we get
| Production Yield (kg/ha) | Number of farms |
| More than or equal to 50 | 100 |
| More than or equal to 55 | 100-2 = 98 |
| More than or equal to 60 | 98-8= 90 |
| More than or equal to 65 | 90-12=78 |
| More than or equal to 70 | 78-24=54 |
| More than or equal to 75 | 54-38 =16 |
From the table obtained draw the ogive by plotting the corresponding points where the upper limits in x-axis and the frequencies obtained in the y-axis are (50, 100), (55, 98), (60, 90), (65, 78), (70, 54) and (75, 16) on
this graph paper. The graph obtained is known as more than type ogive curve.
NCERT Solutions for Class 10 Maths Chapter 14 Statistics
Class 10 Maths Chapter 14, Statistics, is one of the most important of all the chapter present in the textbook. The weightage of this chapter in the CBSE Term II exam is around 11 to 12 marks. On average, there will be 3 questions which could be asked from this chapter and marks will be distributed in a manner of 3+4+4( it could vary as per question).
Topics covered in Chapter 14, Statistics are;
- Mean of Grouped Data
- Mode of Grouped Data
- Median of Grouped Data
- Graphical Representation of Cumulative Frequency Distribution
List of Exercises in class 10 Maths Chapter 14 :
Exercise 14.1 Solutions 9 Question ( 9 long)
Exercise 14.2 Solutions 6 Question ( 6 long)
Exercise 14.3 Solutions 7 Question ( 7 long)
Exercise 14.4 Solutions 3 Question ( 3 long)
NCERT solutions for Class 10 Maths Chapter 14- Statistics are made available for students who want to obtain good marks in this chapter. The methods and procedure to solve the questions have been explained clearly in these NCERT Solutions, such that, students find it easy to understand the fundamentals quickly.
The world is highly data-oriented, in fact, each and every field has a group of data, which represents the relevant information. Statistics is the branch of mathematics which deals with the representation of data in a meaningful way.
You will face many real-life scenarios where the fundamentals of statistics are used to represent a set of data in tabular form or in graphs or in pie charts. There are a number of methods you will learn from this chapter such as, step deviation methods, finding mode and median of grouped data, converting frequency distribution and the relation between mode, mean and median methods, etc. 10th Class NCERT solutions are the best study materials to prepare for the CBSE Term II exam.
Key Features of NCERT Solutions for Class 10 Maths Chapter 14- Statistics
- The solutions for the statistics chapter works as a reference for the students.
- It will help students to score marks against the questions asked from the statistics chapter.
- Students can prepare and do the revision for chapter 14 with this source.
- The questions of statistics are solved by subject experts.
- The content of the material is as per the term-wise CBSE Syllabus (2021-22) and guidelines.
Statistics can also be understood in a much better way by using the other solutions which are provided at RAJ EDUCATION HUB. The solutions are prepared to help students perform well in the CBSE exams.