This page contains the NCERT Statistics for Economicsclass 11 chapter 3 Organisation of Data from the book Statistics for Economics. You can find the solutions for the chapter 3 of NCERT class 11 Statistics for Economics, for the Short Answer Questions, Long Answer Questions and Projects/Assignments Questions in this page. So is the case if you are looking for NCERT class 11 Statistics for Economics related topic Organisation of Data question and answers.
EXERCISES
1. Which of the following alternatives is true?
(i)
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.
(ii)
The frequency distribution of two variables is known as
(a)
Univariate Distribution
(b)
Bivariate Distribution ✔
(c)
Multivariate Distribution
(d)
None of the above
(iii)
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 ✔
(iv)
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
(i)
The correct answer is (a) The average of the upper class limit and the lower class limit. This is because the class midpoint is typically calculated as the average of the upper and lower limits of a class interval.
(ii)
The correct answer is (b) Bivariate Distribution. A bivariate frequency distribution is defined as the frequency distribution of two variables (The name bivariate is derived by the amalgamation of the two words “Bi = Two” and “Variate = Variables”).
(iii)
The correct answer is (d) the class midpoints. In statistical calculations involving classified data, the class midpoint is often used as a representative value of the class.
(iv)
The correct answer is (a) difference between the largest and the smallest observations. Range in statistics is defined as the difference between the maximum and minimum values in a set of data.
2. Can there be any advantage in classifying things? Explain with an example from your daily life.
Yes, there are several advantages to classifying things, as it helps in organizing and analyzing data or items more efficiently. An example from daily life is the organization of books in a library. Libraries classify books into various categories like fiction, non-fiction, science, literature, history, etc. This classification has multiple advantages:
1.
Ease of Finding: By classifying books into specific genres, it becomes much easier for people to find the type of book they are looking for. For instance, if someone is interested in historical novels, they can directly go to the history section.
2.
Better Management: For librarians, it simplifies the task of managing a vast number of books. Knowing exactly where each book belongs reduces the time and effort needed to organize and maintain the collection.
3.
Efficient Space Utilization: Classifying books allows for a more efficient use of space. Similar books can be grouped together in a designated area, making the best use of the available shelving space.
4.
Facilitates Research and Learning: For students and researchers, classification makes it easier to locate resources and reference materials in their area of study, thereby facilitating their learning and research process.
In summary, classification in everyday scenarios like a library not only makes the task of finding and organizing items easier but also optimizes space and supports learning and research activities.
3. What is a variable? Distinguish between a discrete and a continuous variable.
A variable is defined as a characteristic or feature that can take on different values. Variables are critical in the field of statistics as they represent the aspects or qualities of data that are subject to observation and analysis.
Distinguishing between Discrete and Continuous Variables:
Aspect
Discrete Variable
Continuous Variable
Definition
A discrete variable is one that can take on specific, distinct values. These values are countable.
A continuous variable can take on an infinite number of values within a given range.
Value Nature
Typically represents whole numbers.
Can include fractions and decimals; represents measurements.
Example
The number of students in a class (e.g., 30, 31, 32).
Height (e.g., 160 cm, 160.5 cm, 160.51 cm).
In summary, discrete variables consist of distinct, countable values, often whole numbers, while continuous variables can assume any value within a range, including fractional and decimal values.
4. Explain the ‘exclusive’ and ‘inclusive’ methods used in classification of data.
The exclusive and inclusive methods refer to two different approaches used in the classification of data, particularly when dealing with class intervals in frequency distributions.
Exclusive Method:
–
Description: In the exclusive method, each class interval includes the lower limit but excludes the upper limit. This means that the upper limit of a class belongs to the next class.
–
Example: If the class interval is 10-20, it includes values from 10 and goes up to but does not include 20. The value 20 would be included in the next interval, say 20-30.
Inclusive Method:
–
Description: In the inclusive method, both the lower and upper limits of a class interval are included in that class. This method includes the upper limit within the class itself.
–
Example: In a class interval of 10-20, all values from 10 up to and including 20 are part of this class. The next class interval may start from 21.
These methods are vital in statistical data analysis for organizing and interpreting data correctly. The choice between exclusive and inclusive methods depends on the nature of the data and the requirements of the analysis.
(i)
Obtain the range of monthly household expenditure on food.
(ii)
Divide the range into appropriate number of class intervals and obtain the frequency distribution of expenditure.
(iii)
Find the number of households whose monthly expenditure on food is
(a)
less than ₹ 2000
(b)
more than ₹ 3000
(c)
between ₹ 1500 and ₹ 2500
Table 3.2 Monthly Household Expenditure (in Rupees) on Food of 50 Households
1904
1559
3473
1735
2760
2041
1612
1753
1855
4439
5090
1085
1823
2346
1523
1211
1360
1110
2152
1183
1218
1315
1105
2628
2712
4248
1812
1264
1183
1171
1007
1180
1953
1137
2048
2025
1583
1324
2621
3676
1397
1832
1962
2177
2575
1293
1365
1146
3222
1396
1. Range of Monthly Household Expenditure on Food:
–
Maximum Expenditure: ₹ 5090
–
Minimum Expenditure: ₹ 1007
–
Range: ₹ 5090 – ₹ 1007 = ₹ 4083
2. Frequency Distribution of Expenditure:
Using intervals of ₹ 500.
Frequency Distribution Table with Tally Marks:
Expenditure Range (₹)
Tally Marks
Frequency
1000 – 1500
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20
1500 – 2000
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13
2000 – 2500
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6
2500 – 3000
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5
3000 – 3500
{||}
2
3500 – 4000
{|}
1
4000 – 4500
{||}
2
4500 – 5000
0
5000 – 5500
{|}
1
Total
50
3. Number of Households by Expenditure Category:
(a)
Less than ₹ 2000: 20 (from 1000 – 1500) + 13 (from 1500 – 2000) = 33 households
(b)
More than ₹ 3000: 2 (from 3000 – 3500) + 1 (from 3500 – 4000) + 2 (from 4000 – 4500) + 1 (from 5000 – 5500) = 6 households
(c)
Between ₹ 1500 and ₹ 2500: 13 (from 1500 – 2000) + 6 (from 2000 – 2500) = 19 households
6. In a city 45 families were surveyed for the number of Cell phones 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
Based on the survey data provided, the frequency array for the number of cell phones used by the 45 families is as follows:
Number of Cell Phones
Frequency
0
1
1
7
2
15
3
12
4
5
5
2
6
2
7
1
This frequency array shows the distribution of the number of cell phones used by the families in the survey.
7. What is ‘loss of information’ in classified data?
‘Loss of information’ in classified data refers to the reduction in the specificity or detail of data that often occurs when raw data is organized into classes or groups. This concept is crucial in statistical analysis and can be understood through the following points:
1.
Grouping Data: When individual data points are grouped into classes, the specific details of each data point within a class are not distinguished. For example, if students’ marks are classified into ranges, the exact scores within each range are not discernible.
2.
Generalization: Classified data provide a generalized view rather than specific information. This generalization is useful for analysis but can mask the nuances of individual data points.
3.
Analysis Trade-off: While classifying data simplifies analysis and helps in identifying patterns and trends, it can also lead to a loss of detailed information which might be important for certain types of analysis.
4.
Summary Over Specificity: Classification often involves summarizing data, which can lead to a loss of granular information. For instance, knowing the average income in a group does not reveal the income distribution within that group.
In summary, ‘loss of information’ in classified data is a trade-off between the ease of understanding and analyzing large datasets and the detailed specificity of individual data points.
8. Do you agree that classified data is better than raw data? Why?
1.
Ease of Analysis: Classified data is often better for analysis because it organizes raw data into a more manageable form, making it easier to identify patterns and trends.
2.
Simplification: Classification simplifies complex raw data, which can be overwhelming and difficult to interpret, especially when dealing with large datasets.
3.
Summary Information: Classified data provides summary information, like averages, frequencies, and distributions, which is useful for making informed decisions or predictions.
4.
Comparative Study: Classified data facilitates comparative studies. It allows for the comparison of different data sets in a structured manner, which would be challenging with raw data.
5.
Contextual Relevance: The preference for classified over raw data depends on the context. For broad overviews and generalizations, classified data is superior. However, for detailed, specific insights, raw data is more informative.
6.
Loss of Specific Information: While classified data is beneficial for general analysis, it can result in a loss of specific information. This loss can sometimes be critical depending on the nature of the study or analysis.
In conclusion, whether classified data is better than raw data largely depends on the purpose of the analysis. For general, overview analyses, classified data is more advantageous due to its organization and simplicity. However, for in-depth, specific analyses, raw data is essential as it retains all original details.
9. Distinguish between univariate and bivariate frequency distribution.
Here is a comparison between univariate and bivariate frequency distribution in a tabular format:
Aspect
Univariate Frequency Distribution
Bivariate Frequency Distribution
Number of Variables
Involves a single variable.
Involves two variables.
Focus
Focuses on the distribution of one attribute.
Focuses on the relationship between two attributes.
Data Analysis
Analyzes the frequency of one variable.
Analyzes the correlation or association between two variables.
Example
Frequency of marks scored in a test.
Relationship between study hours and marks scored.
In summary, univariate frequency distribution deals with one variable at a time, whereas bivariate frequency distribution involves two variables and their interrelationship.
10. 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
Using the inclusive method with class intervals of 7 (1-7, 8-14, etc.), the frequency distribution for the given data is:
Class Interval
Frequency
1 – 7
17
8 – 14
13
15 – 21
13
22 – 28
11
29 – 35
5
Note: The last class interval for 36 and above is not shown as it falls outside the range of the existing data values.
11. “The quick brown fox jumps over the lazy dog”
Examine the above sentence carefully and note the numbers of letters in each word. Treating the number of letters as a variable, prepare a frequency array for this data.
Based on the sentence “The quick brown fox jumps over the lazy dog” and treating the number of letters in each word as a variable, the frequency array is as follows:
Number of Letters
Frequency
3
4
4
2
5
3
This frequency array shows the distribution of the number of letters in each word of the given sentence.
