CBSE Class 11 Economics Organisation of Data

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CHAPTER - 3: ORGANISATION OF DATA

Short Answer Questions (1 Mark Each)

1. What is meant by classification of data? [1 Mark]

Answer:
1. Classification is the process of arranging raw data into homogeneous groups or classes according to common characteristics.
2. It brings order to complex data.

Teacher's Note:
a) Grouping data based on similarities makes it easy to understand and compare.
b) Ensure students mention homogeneity and grouping in the definition.

2. What is raw data? [1 Mark]

Answer:
1. Raw data refers to unorganized and unclassified data collected directly from the source.
2. It is the initial mass of figures before any statistical treatment.

Teacher's Note:
a) Raw data lacks any systematic arrangement.
b) It serves as the primary input for statistical analysis and classification.

3. Name the different types of data classifications. [1 Mark]

Answer:
1. Geographical classification (spatial).
2. Chronological classification (temporal).
3. Qualitative classification (descriptive).
4. Quantitative classification (numerical).

Teacher's Note:
a) Data can be classified based on space, time, quality, or quantity.
b) Mentioning all four bases is necessary for full credit.

4. What are attributes and variables? [1 Mark]

Answer:
1. Attributes are qualitative characteristics that cannot be measured numerically, such as honesty or gender.
2. Variables are quantitative characteristics that can be measured numerically, such as height or weight.

Teacher's Note:
a) The key distinction is qualitative measurement versus quantitative measurement.
b) Give examples for clarity.

5. What do you mean by qualitative classification? [1 Mark]

Answer:
1. Qualitative classification is the grouping of data according to qualitative characteristics or attributes.
2. Examples include dividing population by literacy, marital status, or religion.

Teacher's Note:
a) Characteristics cannot be measured in quantitative terms.
b) Focus on descriptive attributes.

6. Name the series, which have Class Intervals. [1 Mark]

Answer:
1. Continuous series (or frequency distribution series) has class intervals.

Teacher's Note:
a) Unlike individual or discrete series, continuous series uses ranges of values.
b) Terminology must be precise.

7. What type of error is fatal to statistical results? [1 Mark]

Answer:
1. Error of calculation or error of measurement / bias that goes undetected and distorts the entire conclusion.
2. Gross errors or errors of origin are considered fatal.

Teacher's Note:
a) Errors that invalidate the core premise of data collection lead to incorrect findings.
b) Emphasize systemic or gross errors.

8. For what does \(l_1\) and \(l_2\) in a continuous series mean stand for? [1 Mark]

Answer:
1. \(l_1\) stands for the lower limit of a class interval.
2. \(l_2\) stands for the upper limit of a class interval.

Teacher's Note:
a) These symbols are extensively used in continuous series formulas such as median and mode.
b) Keep the distinction clear between lower and upper bounds.

9. How is mid value calculated? [1 Mark]

Answer:
1. Mid value = \(\frac{\text{Lower Limit} + \text{Upper Limit}}{2}\)

Teacher's Note:
a) Also known as the midpoint or class mark.
b) Essential for calculating the mean of a continuous frequency distribution.

10. What is range? [1 Mark]

Answer:
1. Range is the difference between the highest and lowest values in a given distribution.

Teacher's Note:
a) Formula: Range = Maximum Value - Minimum Value.
b) It is the simplest measure of dispersion.

11. Explain briefly the Exclusive and Inclusive method of continuous series. [1 Mark]

Answer:
1. In the Exclusive method, the upper limit of a class is excluded from that class and included in the next class.
2. In the Inclusive method, both lower and upper limits are included in the same class.

Teacher's Note:
a) Exclusive method handles overlapping limits smoothly.
b) Inclusive method requires adjustment to true limits if gaps exist between classes.

12. How does loss of information take place in a frequency distribution? [1 Mark]

Answer:
1. Grouping raw data into class intervals obscures individual observations.
2. Exact values are lost, and only aggregate frequencies within intervals are known.

Teacher's Note:
a) This is an inherent limitation of continuous frequency distributions.
b) Individual identity of items disappears.

13. What is a 'Bivariate frequency distribution'? [1 Mark]

Answer:
1. A bivariate frequency distribution is the frequency distribution of two variables simultaneously.

Teacher's Note:
a) Used to study the relationship between two characteristics.
b) Typically represented in a two-way cross-classification table.

Short Answer Questions (3 / 4 Marks Each)

1. What are the advantages of classification of data? [3 Marks]

Answer:
1. Simplification and condensation: It presents complex data in a simple, concise, and understandable form.
2. Facilitates comparison: Classification helps highlight similarities, differences, and relationships between different sets of data.
3. Highlights important features: It draws attention to key characteristics and makes statistical analysis and tabulation much easier.

Teacher's Note:
a) State at least three clear points covering condensation, comparison, and analysis.
b) Keep explanations concise and structured.

2. What are the different ways of classification of data? [3 Marks]

Answer:
1. Geographical (Spatial) Classification: Data classified according to location, region, or country.
2. Chronological (Temporal) Classification: Data classified according to time, such as years, months, or days.
3. Qualitative and Quantitative Classification: Data classified based on attributes (qualitative) or measurable numerical values (quantitative).

Teacher's Note:
a) Cover the four primary bases of classification comprehensively.
b) Provide brief descriptions for each category.

3. What are 'discrete' and 'continuous' variables? Differentiate the two variables. [3 Marks]

Answer:
1. Discrete variables take only certain exact or finite values and jump from one value to another without intermediate fractional steps (e.g., number of students).
2. Continuous variables can take any numerical value within a given range, including fractions and decimals (e.g., height, weight).
3. Difference: Discrete variables are counted in whole numbers with gaps, whereas continuous variables are measured on a continuous scale without gaps.

Teacher's Note:
a) Clearly define both variable types.
b) Highlight the presence of fractions and decimals in continuous variables as the core differentiator.

4. 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. [4 Marks]
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

Answer:

Teacher's Note:
a) A frequency array is prepared for discrete variables using tally marks.
b) Sum of frequencies must equal the total number of observations (45).
c) Check counting accuracy carefully for each value from 0 to 7.
d) Proper tabulation format with tally marks awards full credit.

5. Prepare a discrete series table from the following marks secured by 40 students in a test of 10 marks in statistics. [4 Marks]
4 8 6 4 3 2 1 10 9 10
5 4 1 2 5 4 3 2 2 5
8 1 2 5 6 7 6 5 4 5
10 3 3 6 7 9 3 5 7 8

Answer:

Teacher's Note:
a) Discrete frequency distribution lists individual values alongside their respective counts.
b) Total frequency must equal 40 students.
c) Double check tally counting to avoid omission errors.
d) Structure columns neatly with headers.

6. The weights in grams of 20 apples picked from 5 boxes are as under. Construct an inclusive type frequency distribution with a class interval of 5. [4 Marks]
90 95 91 103 101 105 109 97 109 110
92 107 94 106 105 110 92 100 93 91

Answer:

Teacher's Note:
a) Inclusive method retains upper limits inside the same class.
b) Minimum value is 90, maximum value is 110, giving class intervals of length 5.
c) Total frequency equals 20 apples.
d) Ensure class boundaries do not overlap in inclusive series.

7. Prepare from the data given below, prepare a frequency distribution table with class intervals of 0 - 10. [4 Marks]
64 58 62 50 52 63 9 38 42 5
33 55 40 51 48 35 42 41 60 19
76 25 61 48 46 26 11 45 64 28
30 45 53 82 40 18 17 65 55 13
20 40 36 64 50 58 7 15 47 55
70 33 60 48 55 54 15 65 50 60

Answer:

Teacher's Note:
a) Exclusive continuous series is used with class interval width of 10.
b) Boundary values like 10, 20, 30 are included in the higher class interval.
c) Total frequency equals 60 observations.
d) Verify each data entry against tally rows to prevent counting errors.

8. Following are the marks obtained by 20 students in an English test. Prepare a frequency distribution taking class interval of 10 using exclusive and inclusive method. [6 Marks]
5, 16, 17, 17, 20, 21, 22, 22, 22, 25, 25, 26, 26, 30, 31, 31, 34, 35, 42, 48

Answer:

Exclusive Method Frequency Distribution

Inclusive Method Frequency Distribution

Teacher's Note:
a) The exclusive method includes the lower limit but excludes the upper limit.
b) The inclusive method includes both the lower and upper limits of a class.
c) Tally marks simplify the process of counting raw data into frequencies.
d) Total frequency must equal the total number of observations, which is 20.

Long Answer Questions ( 6 Marks Each)

1. What are the steps involved in the preparation of a frequency distribution? Explain. [6 Marks]

Answer:
1. Range determination: Find the difference between the largest and smallest observations to get the total range.
2. Number of classes: Decide the appropriate number of class intervals, usually between 5 and 15 based on data size.
3. Class interval size: Determine the width of the class interval by dividing the range by the chosen number of classes.
4. Choosing the method: Select either the exclusive or inclusive method to frame the class limits.
5. Tally marking: Go through the raw data and assign a tally mark for each observation against its corresponding class interval.
6. Frequency counting: Count the tally marks for each class to arrive at the final frequency distribution table.

Teacher's Note:
a) Proper organization of raw data helps in meaningful statistical analysis.
b) Class intervals should be mutually exclusive and exhaustive where possible.
c) Equal class widths are generally preferred for uniform comparison.
d) The sum of all frequencies must equal the total sample size.

NCERT text book questions

1. Which of the following alternatives is correct? [1 Mark]
(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.

Answer: (a) The average of the upper class limit and the lower class limit.

1. Midpoint formula is (Upper limit + Lower limit) / 2.
2. This represents the central value of a class interval.
3. Hence, the correct option is (a).

Teacher's Note:
a) Midpoints are essential for calculating the arithmetic mean of grouped data.

(ii) The frequency distribution of two variables is known as [1 Mark]
a) Univariate Distribution
b) Bivariate Distribution
c) Multivariate Distribution
d) None of the above

Answer: (b) Bivariate Distribution

1. A distribution involving a single variable is univariate.
2. A distribution involving two variables simultaneously is bivariate.
3. Hence, the correct option is (b).

Teacher's Note:
a) Bivariate distributions are often displayed using a two-way cross-classification table.

2. Use the data of Q.8 that relate to test marks by 20 students in an English test. Answer the following:
a) Obtain the range of marks. [1 Mark]

Answer:
1. Maximum value = 48
2. Minimum value = 5
3. Range = Maximum value - Minimum value = 48 - 5 = 43.

Teacher's Note:
a) Range is the simplest measure of dispersion in statistical data.

b) Divide the range into appropriate number of class intervals and obtainthe frequency distribution of marks [3 Marks]

Answer:
1. Taking class interval of width 10, the suitable exclusive classes are 0 - 10, 10 - 20, 20 - 30, 30 - 40, and 40 - 50.
2. Tallying the given 20 values into these intervals gives frequencies of 1, 3, 9, 6, and 2 respectively.
3. The resulting frequency distribution matches the exclusive frequency table prepared in Question 8.

Teacher's Note:
a) Class width should cover all data values smoothly without leaving gaps.
b) Ensure that boundary values are placed consistently using exclusive convention.
c) Verify that the sum of all frequencies equals 20.

c) Find the number of students whose marks in the test are: [2 Marks]
(i) Less than 20

Answer:
1. Marks less than 20 include class intervals 0 - 10 and 10 - 20.
2. Frequency for 0 - 10 is 1 and for 10 - 20 is 3.
3. Total number of students = 1 + 3 = 4.

Teacher's Note:
a) Cumulative frequency concept is applied here to sum frequencies up to the given threshold.
b) Values falling exactly on the upper boundary 20 are excluded in the exclusive method.

(ii) More than 25

Answer:
1. Marks more than 25 include values from 26 onwards up to 48.
2. From the raw data, marks greater than 25 are 26, 26, 30, 31, 31, 34, 35, 42, 48.
3. Counting these values gives a total of 9 students.

Teacher's Note:
a) Direct counting from raw data or subtracting lower cumulative frequency can be used.
b) Care must be taken to include boundary values correctly as specified.