CBSE NCERT Class XI (11th)  Economics
Ncert Solutions of Statistics for Economics for Chapter 3 : Organisation of Data
Q1 :
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 :
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.
Q2 :
The frequency distribution of two variables is known as
(a) Univariate Distribution
(b) Bivariate Distribution
(c) Multivariate Distribution
(d) None of the above
Answer :
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.
Q3 :
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
Answer :
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.
Q4 :
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
Answer :
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.
Q5 :
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
Answer :
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
Q6 :
Can there be any advantage in classifying things? Explain
with an example from your daily life.
Answer :
Yes, there are many advantages of classifying things. The
following are the advantages associated with classification:
1. 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.
2. Quick Information Information can be
easily collected from the classified things.
3. 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 nonhaphazard manner.
Q7 :
What is a variable? Distinguish between a discrete and a
continuous variable.
Answer :
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.

Q8 :
Explain the 'exclusive' and 'inclusive' methods used in
classification of data.
Answer :
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, 010, 1020, 2030 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, 15, 610, 1115 and so
on. The interval 15 includes both the limits i.e. 1 and 5.
Q9 :
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.
Answer :
Calculation of Range
Range = Highest Value  Lowest Value
Highest Value = 5090
Lowest Value = 1007
So, Range = 5090  1007 = 4083
Q10 :
Divide the range into appropriate number of class
intervals and obtain the frequency distribution of expenditure.
Answer :
(ii) Preparing Tally Marks
Class Intervals

Tally Marks

Frequency

1000  1500


20

1500  2000

13


2000  2500

Q11 :
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
Answer :
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
Q12 :
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

Answer :
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

Q13 :
What is 'loss of information' in classified data?
Answer :
'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.
Q14 :
Do you agree that classified data is better than raw
data?
Answer :
The classified data has following advantages over the raw
data.
1. ComprehensiveRaw data are large and
entangled, whereas classified data are comprehensive and easily manageable.
2. Quick Information It is troublesome to
pick up information from unclassified data. Information can be easily collected
from the classified data.
3. Conclusions  Classification facilitates
comparisons and helps in drawing fast conclusions or inferences.
4. 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.
Q15 :
Distinguish between Univariate and Bivariate frequency
distribution.
Answer :
Univariate Frequency Distribution

Bivariate Frequency Distribution

The word ร¢รข‚¬รลUni' 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 ร¢รข‚¬รลBi' 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.

Q16 :
Prepare a frequency distribution by inclusive method
taking class interval of 7 from the following data:
28

17

15

22

29

21

Answer :
Class Interval

Tally marks

Frequency

0  7

15


8  15

15


16  23

14


24  31

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