NCERT Solutions for Class 11 Economics (Statistics for Economics) Chapter 3 Organisation of Data

NCERT
SOLUTIONS
CLASS - 11th

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Book : Statistics for Economics Ncert Solutions | Chapter - 3 Statistics

Class : 11th
Subject : Statistics
Chapter : 3
Chapter Name : Organisation of Data

Q1 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

Answer.
(i) Option (a) is the correct answer.
Class Midpoint is given as (Upper Class Limit + Lower Class Limit)/2.

(ii) Option (b) is the correct answer.
Since there are only two variables, the frequency distribution is called a bivariate
distribution.

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Book : Statistics for Economics Ncert Solutions | Chapter - 3 Statistics

(iii) Option (d) is the correct answer.
Since the actual values in a range are difficult to determine accurately, the class
midpoints are calculated to give a fairly accurate result.

(iv) Option (a) is the correct answer.
Range is given by (Largest value – Smallest value).
Note: Option (b) seems to be the correct answer too, because the difference is taken
without any algebraic expressions. However, on the safe side option (a) will be
accepted.

Page : 37 , Block Name : Exercises

Q2 Can there be any advantage in classifying things? Explain with an
example from your daily life.

Answer. Yes. These are the following advantages in classifying things :
1. Easy Interpretation – The data can be interpreted very easily if it is classified
rather than scattered.
2. Less Time Consuming – The data, if classified takes lesser time to analyse and
derive conclusions.
3. Visualisation of Relation – The data when classified is easy to visualise and
certain relations between the data can be derived by a simple look at the data.
For example, a chemist has to deal with a lot of medicines everyday. Therefore, he
sorts the medicines alphabetically to find them easily.

Q3 What is a variable? Distinguish between a discrete and a continuous
variable.

Answer. A variable is a quantity that can take multiple values from a range of values,
one at a time. It is of two types — discrete and continuous.

Discrete Variable Continuous Variable

1. It takes values only in whole It takes values from a range, and can
numbers. be fractional.

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Book : Statistics for Economics Ncert Solutions | Chapter - 3 Statistics

2. The increase in values is in the form The increase can be fractional or in
of jumps. whole numbers, but no jump occurs.

3. Example: Number of people that can Example: Age of the students of a class
be accommodated in a bus

Q4 Explain the ‘exclusive’ and ‘inclusive’ methods used in classification of
data.

Answer. In the exclusive method of classification of data, the values are taken from the
lower limit of the class interval but the upper limit is excluded. The upper limit of one
class interval becomes the lower limit of the succeeding class interval. For example,
class intervals as 0-5, 5-10, 10-15, etc. are exclusive.

In the inclusive method, both the upper limit as well as the lower limit of the class
interval is taken into consideration. The values of class intervals do not overlap in this
case. For example, class intervals such as 0-4, 5-9, 10-14, etc. are inclusive.

Q5 Use the data in Table 3.2 that relate to monthly household expenditure (in Rs) on
food of 50 households and
(i) Obtain the range of monthly household expenditure on food.

(ii) Divide the range into appropriate number of class intervals and obtain

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Book : Statistics for Economics Ncert Solutions | Chapter - 3 Statistics

the frequency distribution of expenditure.

(iii) 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.
(i) Range = Highest Value – Lowest Value
= 5090 – 1007
= 4083

(ii) The Frequency Distribution is given below:

Monthly Household Tally Bars Frequency Distribution of
Expenditure Class Expenditure
Intervals

1000-1500 20

1500-2000 13

2000-2500
06
2500-3000
05
3000-3500
02
3500-4000
II 01
4000-4500
I 02
4500-5000
- 00
5000-5500
I 01

50

(iii) (a) The number of households whose monthly expenditure on food is less than Rs
2000 = 33

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Book : Statistics for Economics Ncert Solutions | Chapter - 3 Statistics

(iii) (b) The number of households whose monthly expenditure on food is more than Rs
3000 = 6

(iii) (c) The number of households whose monthly expenditure on food is between Rs
1500 and Rs 2500 = 19

Q6 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.

Answer. The frequency array of the given data is as follows:

Number of Domestic Appliances Number of Households

0 1

1 7

2 15

3 12

4 5

5 2

6 2

7 1

Total 45

Q7 What is ‘loss of information’ in classified data?

Answer. The loss of information in a classified data means that the actual values are
lost when the data is classified into a compact volume. The observations lose their

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Book : Statistics for Economics Ncert Solutions | Chapter - 3 Statistics

individuality and assume the value equal to the average of the class size, i.e. class
midpoint. Therefore, the data is not available for study. Only their frequency is studied in
case of classified data.

Q8 Do you agree that classified data is better than raw data? Why?

Answer. Yes, despite some drawbacks, classified data is better than raw data due to the
following reasons:
1. Classified data is easy to analyse.
2. Classified data saves time and hence a comprehensive study can be performed
in a short time.
3. Classified data is easy to pass on, so that others may understand what has been
interpreted and concluded after the analysis.

Q9 Distinguish between univariate and bivariate frequency distribution.

Answer. In a univariate frequency distribution, there is only one variable whose
frequency distribution is studied. For example, the money spent by a person in a day on
various things.

In a bivariate frequency distribution, there are two variables whose frequency
distribution is studied. For example, height and weight comparison of the students in a
class.

Q10 Prepare a frequency distribution by inclusive method taking class interval of 7 from
the following data.

Answer. The Frequency distribution table is given below:

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Book : Statistics for Economics Ncert Solutions | Chapter - 3 Statistics

Class Tally marks Frequency
Interval

0–7 15

8 – 15 15

16 – 23 14

24 – 31 11

32 – 39 5

Total 60

Q11 “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.

Answer. The frequency distribution table is given below :

Number of Letters Tally Marks Frequency

1 – 0

2 – 0

3 |||| 4

4 || 2

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Book : Statistics for Economics Ncert Solutions | Chapter - 3 Statistics

5 ||| 3

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