NCERT Solutions Class 11, Economics, Statistics for Economics, Chapter- 3, Organisation of Data
1. Which of the following alternatives is true?
(i) The class mid-point 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
Solution:
(a) the average of the upper-class limit and the lower class limit
The class mid-point refers to the middle value of a class. It is the middle value between the upper class limit and the lower class limit of a class and is computed as
Class Mid-Point = \(\frac{\text{(Lower Class Limit + Upper Class Limit)}}2\)
(ii) The frequency distribution of two variables is known as:
(a) Univariate Distribution
(b) Bivariate Distribution
(c) Multivariate Distribution
(d) None of the above
Solution:
(b) Bivariate Distribution
Bi refers to two and therefore, the frequency distribution of two variables is called a Bivariate Distribution.
(iii) Statistical calculation 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 mid-points
Solution:
(d) the class mid-points
The class mid-points of each class is used to present the class and thus, it is used in further estimates after the raw data and facts are grouped into classes.
(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
Solution:
(a) difference between the largest and the smallest observations
The range is the difference between the largest value and the smallest value of the variable. A large range depicts the values of the variable that are widely spread.
2. Can there be any advantage in classifying things? Explain with an example from your daily life.
Solution:
Classification means organising and arranging the similar data or homogenous data into groups. Classification of objects saves the valuable cost in terms of time, money and effort. Classification is done to group the homogenous things. For example, one classify his/her wardrobe into different types of dresses as per the occasions. They put school uniform, party wears, night wears and casual daily wears separately. This will aids in an orderly and systematic arrangement of clothes and one can easily find out the clothes they want at a specific time without much searching. Hence, it is clear that classification not only saves time but also saves labour and aids to produce the desired outcomes.
3. What is a variable? Distinguish between a discrete and a continuous variable.
Solution:
A characteristic that takes different values at different time intervals and in different situations is known as variable. It always keeps changing. Different variables changes based upon the way they vary. They are further divided into two parts, i.e.,
S. No. |
Discrete Variable |
Continuous Variable |
(i) |
A discrete variable deals only with whole numbers. |
A continuous variable deals with any numerical value. |
(ii) |
Discrete variables only takes the finite value and does not deals with the intermediate value between them. |
Continuous variables take any conceivable value or intermediate value. |
(iii) |
For examples, number of residents in a colony, number of workers in a factory, number of students in a class etc. |
For examples, weight, height, distance, percentage scored in a test etc. |
4. Explain the ‘exclusive’ and ‘inclusive’ methods used in classification of data.
Solution:
In the exclusive method, the classes are formed such that the lower class limit of one class becomes the upper class limit of the preceding class. Therefore, the continuation of the data is maintained. Also, in this method, the upper class limit of a class is not included, but the lower class limit is included in the interval.
In simple terms, if an observation is exactly the same as of the upper class limit, then it will not be included in that class but will be included in the next class. In contrast, if an observation is exactly the same as of the lower class limit, then it will be included in that class only. For example, if the class intervals are 0-10, 10-20, 20¬30 and so on, then a value of 20 will be included in the interval 20-30 and not in the interval 10-20.
Inclusive Method is just the opposite of Exclusive Method. The inclusive method does include the upper class limit also. Therefore, both class limits are included in the class interval. For example, if the class intervals are 0-10, 11-20, 21-30 and so on, then a value of 20 will be included in the interval 11-20.