Question-1
Solution:
Yes. There are many advantages in classifying things.
Infact, we are following classification methodology with out our knowledge in our day-today life.
(i.e) arranging currency notes in our purse.
Classifying utensils according to their shapes and usages.
Question-2
Solution:
Variable does not tell us that how it varies. There are two types of variables. They are discrete and continuous variable.
Continuous variable:
A continuous variable can take any numerical value. It may take integral values (1, 2, 3, 4, ...), fractional values (1/2, 2/3, 3/4, ...), and values that are not exact fractions ( =1.414, =1.732, … , =2.645).
For example, the height of a student, as he/she grows say from 90 cm to 150 cm, would take all the values in between them.
It can take values that are whole numbers like 90cm, 100cm, 108cm, 150cm. It can also take fractional values like 90.85 cm, 102.34 cm and 149.99cm etc. that are not whole numbers. Thus the variable “height” is capable of manifesting in every conceivable value and its values can also be broken down into infinite gradations.
Other examples of a continuous variable are weight, time, distance, etc.
Discrete variable:
Unlike a continuous variable, a discrete variable can take only certain values.
Its value changes only by finite “jumps”. It “jumps” from one value to another but does not take any intermediate value between them.
For example, a variable like the “number of students in a class”, for different classes, would assume values that are only whole numbers. It cannot take any fractional value like 0.5 Because “half of a student” is absurd. Therefore it cannot take a value like 25.5 between 25 and 26. Instead its value could have been either 25 or 26.
What we observe is that as its value changes from 25 to 26, the values in between them, the fractions are not taken by it. But do not have the impression that a discrete variable cannot take any fractional value.
Question-3
Solution:
Exclusive method:
Under this method, the upper class limit is excluded but the lower class limit of a class is included in the interval. Thus an observation that is exactly equal to the upper class limit, according to the method, would not be included in that class but would be included in the next class. On the other hand, if it were equal to the lower class limit then it would be included in that class.
For Example,
In the class 800-899, the upper class limit 800 is included and the lower class limit 899 is excluded.
Inclusive method:
The Inclusive Method does not exclude the upper class limit in a class interval. It includes the upper class in a class. Thus both class limits are parts of the class interval.
For Example,
In the class 800–899, both upper class limit and the lower class limit 800 and 899 are included.
Question-4
Solution:
(i) The range of monthly household expenditure on food is 5090 – 1007 = Rs. = 4083
(ii) Here, we are following Exclusive method for classification of data.
Household expenditure on food class |
Frequency |
1007-2007 2007-3007 3007-4007 4007-5007 5007-6007 |
32 11 3 2 1 |
Total |
50 |
(iii) The number of households whose monthly expenditure on food which is less than Rs.2000 are 33.
(iv) The number of households whose monthly expenditure on food which is more than Rs. 3000 are 17.
(v) The number of households whose monthly expenditure on food which is in between Rs 1500 and Rs 2500 are 18.
Question-5
Solution:
Type of domestic appliance |
No of families used domestic appliances (frequency) |
0 1 2 3 4 5 6 7 |
1 7 15 12 5 2 2 1 |
Total |
45 |
Question-6
Solution:
All values in the class 20-30 are assumed to be equal to the middle value of the class interval or class mark (i.e. 25).
Further statistical calculations are based only on the values of class mark and not on the values of the observations in that class. This is true for other classes as well.
Thus the use of class mark instead of the actual values of the observations in statistical methods involves considerable loss of information.
Question-7
Solution:
Yes, the classified data is better than the raw data.
Because, the raw data consist of observations on variables. Each unit of raw data is an observation.
The raw data are summarised, and made comprehensible by classification. When facts of similar characteristics are placed in the same class, it enables one to locate them easily, make comparison, and draw inferences without any difficulty.
For Example,
Suppose you want to know the performance of students in mathematics and you have collected data on marks in mathematics of 100 students of your school. If you present them as a table. It is called Raw or unclassified data. (i.e) numbers are not arranged in any order. Now if you are asked what are the highest marks in mathematics or lowest marks in mathematics, then we cannot answer immediately. In such a case, we need to arrange the data in descending order or in ascending order. This arrangement is called classified data.
Finally, the process of arranging the huge masses of data in a proper way is called classification. Or it is defined as “the process of arranging or bringing together all the enumerated individuals or items under separate heads or classes according to some common characteristics possessed by them”.
Question-8
Solution:
Univariate frequency distribution |
Bivariate frequency distribution |
The frequency distribution of a single variable is called a Univariate Distribution.
We cannot compare a variable with other one. |
A Bivariate Frequency Distribution is the frequency distribution of two variables.
We can compare between two variables. |
Question-9
Solution:
Class |
Frequency |
1-7 8-14 15-21 22-28 29-35 36-42 |
15 11 14 10 6 2 |
Question-10
Solution:
When we classify raw data of a continuous variable as a frequency distribution, we in effect, group the individual observations into classes. The value of the upper class limit of a class is obtained by adding the class interval with the value of the lower class limit of that class.
For example, the upper class limit of the class 10– 20 is 10 + 10 = 20 where 10 is the lower class limit and 10 is the class interval. This method is repeated for other classes as well.
But how do we decide the lower class limit of the first class? That is to say, why 0 is the lower class limit of the first class: 0–10? It is because we chose the minimum value of the variable as the lower limit of the first class.
In fact, we could have chosen a value less than the minimum value of the variable as the lower limit of the first class. Similarly, for the upper class limit for the last class we could have chosen a value greater than the maximum value of the variable.