NCERT Solutions for Class 11 Statistics Chapter 3: We will assist you to understand the significance of data organization. You will learn how to classify data into different groups so that they may compare them later in this chapter. This lesson has been included in the NCERT syllabus to help students gain a basic understanding of the subject so that you can study more about it in the future.
Students may understand the foundation of this chapter by following NCERT Solutions For Class 11 Statistics Chapter 3 helping them to do well in upcoming exams.
NCERT Solutions For Class 11 Statistics Chapter 3 PDF
NCERT Solutions For Statistics Class 11 Ch 3
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NCERT Solutions For Class 11 Statistics Chapter 3: Overview
Students learn about data classification by consulting NCERT Solutions For class 11 Statistics Chapter 3. They learn how to sort data by location, similarity, and other factors. This chapter, Data Organization, is included in the NCERT syllabus to provide students with a foundation in statistics.
Students will be able to grasp the concept behind this lesson much faster with the help of the various questions and exercises in this chapter. These NCERT Solutions For Class 11 Statistics chapter 3 economics have been written in an examination manner. This is done to help kids feel less apprehensive during tests.
NCERT Solutions For Class 11 Statistics For Economics Chapter 3 | Exercises
Exercise 1: Organisation of Data
Students are given a thorough introduction to data organisation in this section of the chapter. This part contains a brief summary of the topic as well as various images to aid comprehension of the course.
Exercise 2: Classification
The next section contains a basic summary of data classification requirements. They must first know why data must be separated into different groups before moving on to understanding how it can be done.
Exercise 3: Objective and Characteristics of Classification
Data classification is crucial because it teaches students how to divide data into categories and examine it later. It also helps with understanding the differences between different data groupings and how data can be separated.
Exercise 4: Basis of Classification
Students are taught how to segregate data based on location, quality, amount, and other factors while striving to grasp the process of data categorization. The way you divide data into groups is usually determined by the outcome you want to achieve.
Exercise 5: Types of statistical Series
Students will need to grasp the numerous types of statistical series that they can generate after properly segregating and classifying data. It is the technique of arranging data in a specified sequence to make the analysis process more efficient.
Exercise 6: Types of Frequency Distribution
Students will gain knowledge of the frequency distribution by studying several types of statistical series. They will learn about exclusive series, inclusive series, cumulative frequency, and other concepts in this section of the chapter. Students must complete the exercises in this part in order to better understand the lesson.
Access NCERT Solutions For Class 11 Statistics Chapter 3
1. The class midpoint is equal to:
(a) The average of the upper class limit and the lower class limit.
(b) The product of upper class limit and the lower class limit.
(c) The ratio of the upper class limit and the lower class limit.
(d) None of the above.
The option (a) is correct.
The class midpoint is equal to the average of the upper class limit and the lower class limit. It is known by adding the values of upper and lower limits and dividing the total by 2.
2. The frequency distribution of two variables is known as
(a) Univariate Distribution
(b) Bivariate Distribution
(c) Multivariate Distribution
(d) None of the above
The option (b) is correct.
The frequency distribution of two variables is known as Bivariate Frequency Distribution. In other words, Bivariate Frequency Distribution shows the series of statistical data having frequencies of two variables such as the data on income and expenditure of the households.
3. Statistical calculations in classified data are based on
(a) the actual values of observations
(b) the upper class limits
(c) the lower class limits
(d) the class midpoints
The option (d) is correct.
The calculations in classified data or continuous series are based on the class midpoints. The items in a continuous series cannot be exactly measured. Consequently, the class midpoints are calculated.
4. Under Exclusive method,
(a) the upper class limit of a class is excluded in the class interval
(b) the upper class limit of a class is included in the class interval
(c) the lower class limit of a class is excluded in the class interval
(d) the lower class limit of a class is included in the class interval
The option (a) is correct.
A series in which upper limit of one class becomes the lower limit of the succeeding class interval is called exclusive series. In such series, the frequencies of the lower limit are included in that particular class whereas the frequencies of the upper limit are excluded.
5. Range is the
(a) difference between the largest and the smallest observations
(b) difference between the smallest and the largest observations
(c) average of the largest and the smallest observations
(d) ratio of the largest to the smallest observation
The option (a) is correct.
Range is defined as the difference between the largest and the smallest observations.
Algebraically,
R = H – L
Where,
R denotes range
H is the highest value
L is the lowest value
6. Can there be any advantage in classifying things? Explain with an example from your daily life.
Yes, there are many advantages of classifying things. The following are the advantages associated with classification:
- Saves Time and Energy-Classification of things not only saves our time but also our energy which would otherwise be utilised in searching from entire lot of things.
- Quick Information-Information can be easily collected from the classified things.
- Easy Classification-Classification facilitates comparisons and helps in drawing fast conclusions or inferences.
The advantage of classification can be better understood with the help of a daily life example. A post office on the regular basis sorts letters and then classifies them according to various attributes. Letters are classified first according to the states, then according to the cities and streets. Thus, this process of classification helps the postman to deliver posts quickly, efficiently and in a non-haphazard manner.
7. What is a variable? Distinguish between a discrete and a continuous variable.
A measurable characteristic whose value changes overtime is called variable. It refers to that quantity which keeps on changing and which can be measured by some unit. For example, if we measure the height of students of a class, then height is regarded as a variable. A variable can be either discrete or continuous.
|
Discrete Variable |
Continuous Variable |
|
A variable that takes only whole number as its value is called discrete variable. These variables increase in jumps or in complete numbers. For example- Number of people in a family, number of students in a class, etc. |
A variable that can take any value, within a reasonable limit is called a continuous variable. These variables assume a range of values or increase in fractions and not in jumps. For example- age, height, weight, etc. |
8. Explain the ‘exclusive’ and ‘inclusive’ methods used in classification of data.
Exclusive Method– This method is used for those series in which the upper limit of one class becomes the lower limit of the next class. It is called as exclusive series because the frequencies of the upper limit of a class interval are not included in that particular class. In such type of series, the upper limit of one class becomes the lower limit of the next class, for example, 0–10, 10–20, 20–30 and so on. The upper limit is excluded but the lower limit is included in the class interval. This method is most appropriate for data of continuous variables.
Inclusive Method– Under this method of classification of data, the classes are formed in such a manner that the upper limit of a class interval does not repeat itself as the lower limit of the next class interval. In such a series, both the upper limit and the lower limit are included in the particular class interval, for example, 1–5, 6–10, 11–15 and so on. The interval 1–5 includes both the limits i.e. 1 and 5.
9. Use the data in Table 3.2 that relate to monthly household expenditure (in Rs) on food of 50 households and obtain the range of monthly household expenditure on food.
Calculation of Range
Range = Highest Value – Lowest Value
Highest Value = 5090
Lowest Value = 1007
So, Range = 5090 – 1007 = 4083
10. Divide the range into appropriate number of class intervals and obtain the frequency distribution of expenditure.
(ii) Preparing Tally Marks
|
Class Intervals |
Tally Marks |
Frequency |
|
1000 – 1500 |
20 |
|
|
1500 – 2000 |
13 |
|
|
2000 – 2500 |
06 |
|
|
2500 – 3000 |
05 |
|
|
3000 – 3500 |
02 |
|
|
3500 – 4000 |
01 |
|
|
4000 – 4500 |
02 |
|
|
4500 – 5000 |
– |
00 |
|
5000 – 5500 |
01 |
|
|
Total |
|
50 |
11. Find the number of households whose monthly expenditure on food is
(a) less than Rs 2000
(b) more than Rs 3000
(c) between Rs 1500 and Rs 2500
- a) Number of households whose monthly expenditure on food is less than Rs 2000
= 20 + 13 = 33
- b) Number of households whose monthly expenditure on food is more than Rs 3000
= 2+1+2+0+1 = 6
- c) Number of households whose monthly expenditure on food is between Rs 1500 and Rs 2500
= 13 + 6 = 19
12. In a city 45 families were surveyed for the number of domestic appliances they used. Prepare a frequency array based on their replies as recorded below.
|
1 |
3 |
2 |
2 |
2 |
2 |
1 |
2 |
1 |
2 |
2 |
3 |
3 |
3 |
3 |
|
3 |
3 |
2 |
3 |
2 |
2 |
6 |
1 |
6 |
2 |
1 |
5 |
1 |
5 |
3 |
|
2 |
4 |
2 |
7 |
4 |
2 |
4 |
3 |
4 |
2 |
0 |
3 |
1 |
4 |
3 |
Frequency Array of appliances being used by households
|
No. of Domestic Appliances |
No. of Households |
|
0 |
1 |
|
1 |
7 |
|
2 |
15 |
|
3 |
12 |
|
4 |
5 |
|
5 |
2 |
|
6 |
2 |
|
7 |
1 |
|
Total |
45 |
13. What is ‘loss of information’ in classified data?
‘Loss of information’ is a major drawback of the classified data. The classification or grouping of raw data into classes makes it more concise and understandable. But simultaneously there exists loss of information. The calculations involved in the classified data or the continuous series are based on the class midpoints. The items in such series cannot be exactly measured and consequently, an individual observation loses its importance during the statistical calculations. Further, the statistical calculations are based on the values of the class marks, ignoring the exact observations of the data leading to the problem of loss of information.
14. Do you agree that classified data is better than raw data?
The classified data has following advantages over the raw data.
- Comprehensive-Raw data are large and entangled, whereas classified data are comprehensive and easily manageable.
- Quick Information-It is troublesome to pick up information from unclassified data. Information can be easily collected from the classified data.
- Conclusions –Classification facilitates comparisons and helps in drawing fast conclusions or inferences.
- Saves Time and Energy-Classified data not only save our time but also our energy, which would otherwise be utilised in searching from entire lot of things.
15. Distinguish between univariate and bivariate frequency distribution.
|
Univariate Frequency Distribution |
Bivariate Frequency Distribution |
| The word ‘Uni’ means one. A series of statistical data showing the frequency of only one variable is called Univariate Frequency Distribution. In other words, the frequency distribution of single variable is called Univariate Frequency Distribution. For example- income of people, marks scored by students, etc. | The word ‘Bi’ means two. A series of statistical data showing the frequency of two variables simultaneously is called Bivariate Frequency Distribution. In other words, the frequency distribution of two variables is called Bivariate Frequency Distribution. For example- sales and advertisement expenditure, weight and height of individuals, etc. |
16. Prepare a frequency distribution by inclusive method taking class interval of 7 from the following data:
|
28 |
17 |
15 |
22 |
29 |
21 |
23 |
27 |
18 |
12 |
7 |
2 |
9 |
4 |
|
1 |
8 |
3 |
10 |
5 |
20 |
16 |
12 |
8 |
4 |
33 |
27 |
21 |
15 |
|
3 |
36 |
27 |
18 |
9 |
2 |
4 |
6 |
32 |
31 |
29 |
18 |
14 |
13 |
|
15 |
11 |
9 |
7 |
1 |
5 |
37 |
32 |
28 |
26 |
24 |
20 |
19 |
25 |
|
19 |
20 |
6 |
9 |
|
|
|
|
|
|
|
|
|
|
|
Class Interval |
Tally marks |
Frequency |
|
0 – 7 |
15 |
|
|
8 – 15 |
15 |
|
|
16 – 23 |
14 |
|
|
24 – 31 |
11 |
|
|
32 – 39 |
5 |
|
|
Total |
|
60 |
Access Other Chapters of NCERT Solutions For Class 11 Statistics
You can download the PDF of NCERT Solutions For Class 11 Statistics other chapters:
- Chapter-1 Introduction
- Chapter-2 Collection Of Data
- Chapter-3 Organization Of Data
- Chapter-4 Presentation of Data
- Chapter-5 Measures of Central Tendency
- Chapter-6 Measures of Dispersion
- Chapter-7 Correlation
- Chapter-8 Index Numbers
We have provided all the important above in the article regarding the CBSE NCERT Solutions For Class 11 Statistics Chapter 3. If you have any queries, you can mention them in the comment section.
FAQ (Frequently Asked Questions): NCERT Solutions for Class 11 Statistics Chapter 3
What is the advantage of classifying things, explain?
Data classification is the process of organizing data by categorizing it into different groupings. In order to begin this procedure, students must first determine what distinguishes these data from one another. The data is then meant to be grouped based on similarity. Students can better analyze data if they separate it.
What are variables, and explain discrete as well as continuous variables?
Variation refers to numerical values that change over time and in response to circumstances. It got its name from one of its distinguishing characteristics: it is always changing or fluctuating. Discrete and continuous variation are the two types of variation that you will study in this session. Whole numbers that tend to increase indefinitely are referred to as discrete variables.
A continuous variable, on the other hand, can take any numerical value and can grow indefinitely. The number of industrial workers, for example, is a discrete variable, whereas the height and weight of these workers are continuous variables.
What are the inclusive and exclusive methods of data classification?
Students can also use exclusive and inclusive data to classify data. A numbered table is an exclusive frequency distribution. The first value’s upper-class limit becomes the second value’s lower-class limit in this case. The inclusive technique, on the other hand, takes into account both the series’ upper and lower class limits. This provides for proper division without causing the students any misunderstanding. The NCERT Solution concentrates on this portion because it accounts for the majority of the marks. This is why, in order to achieve a high grade, students must thoroughly study this section of the chapter.
What is an inclusive series?
An inclusive series is a series that includes all the items until the upper limit.