Economics 3 Marks Question

When the whole range of values is classified in some groups in the form of intervals, then each such interval is known as class interval. For example, we may want to classify a group of people according to age group. Here, the class intervals may be 15 - 19 years, 20 – 24 years, 25 – 29 years etc.
The difference between the upper and lower boundaries of a class interval is called the magnitude of the class interval.
The numerical figures used to specify the lower and upper limits of a 'class interval' are called class limits. For example, if the class interval is 15 – 19 years, the lower class limit is 15 and the upper limit is 19 in this case.

Yes, classified data is better than raw data. This is because:

1. Simplification: Raw data are large and difficult to handle. On the other hand, classification facilitates the arrangement of data in a presentable form which appears to be brief and simple for analysis.
2. Effective: Raw data is not easy to understand and cannot conclude any meaningful information for the study. On the other hand, classification enhances the usage of data as it brings out similarity within the diverse set of data. Thus, classification of things makes it more effective.
3. Save time: Raw data is huge to search for particular information, whereas classified data saves time when searching for information.

The objectives of classification of data are:

1. To condense the mass of data in a brief and simple form, so as to make them easily understandable.
2. To clearly reveal the points of similarities and dissimilarities in the statistical data. e.g., married and unmarried, employed and unemployed.
3. To facilitate the comparison of data.
4. To present data scientifically.
5. To make the data attractive and effective.
6. To provide basis for tabulation. No tabulation is possible without classification.

The general guidelines for the construction of a frequency distribution are:

1. The number of classes should neither be too small nor too large, preferably between 5 to 15.
2. All class intervals should be of equal size.
3. Open-end classes should be avoided.
4. We should preferably classify the data into exclusive series (if it is not specified otherwise).
5. We should avoid unequal sized class intervals.

Array: 15, 15, 15, 20, 20, 20, 25, 25, 25, 25, 30, 30, 30, 30, 30, 35, 35, 40, 40, 40, 40, 45, 50, 50, 50

Here, we can convert given data into frequency distribution and cumulative frequency distribution by using tally bar and inclusive series.

1. The frequency distribution of given data is shown below.

2. To form cumulative frequency distribution (less than) of the given distribution, exclusive group will be formed.

Class Interval	Exclusive Group	Frequency (f)
20-29	19.5-39.5	2
30-39	29.5-39.5	4
40-49	39.5-49.5	8
50-59	49.5-59.5	6
60-69	59.5-69.5	5
Total		25

Cumulative frequency distribution (less than) is given below.

Class Interval	Cumulative Frequency (cf)
Less than 29.5	2
Less than 39.5	6
Lesss than 49.5	14
Less than 59.5	20
Less than 69.5	25

In the given question, as the class intervals of 2nd, 3rd and 4th classes are uniform, i.e., 10 we can therefore assume that the class-intervals of open-end classes are also equal to 10.
This means that the lower limit of the first class is 10 - 10 = 0 and the upper limit of the last class is 40 + 10 = 50.

There are two methods of classifying data according to class intervals, namely,

1. Exclusive method: Under this method, upper limit of the class is excluded. The upper limit of class interval is the lower limit of the next class, e.g.,

Marks	0 - 10	10 – 20	20 – 30
No. of Students	2	5	2

We include those students in first group whose marks are 0 or more but less than 10. If the marks of a student are 10, he is not included in the first group but in the second group, i.e., 10 - 20.

1. Inclusive method: Under this method, both the lower limit and the upper limit is included in the respective class, e.g.,

Marks	0 - 9	10 – 19	20 – 29
No. of Students	2	5	2

We include students in the first group whose marks are between 0 and 9. If the marks of a student are 10, he is included in the next group, i.e., 10 – 19.

S. No.	Difference between Individual, Discrete and Continuous series
1.	Individual Series	Discrete Series	Continuous Series
2.	In individual series, there is only one frequency for each item.	In case of discrete series, there is frequency of more than one for each item.	In case of continuous series, there is frequency of more than one for each item.
3.	Individual series has one column and that is of observations.	In discrete there are two columns, one for frequency and second for variable. Variable is a number.	In continuous series also, there are two columns as in discrete series but variable is in the form of a class.
4.	Values are given after a definite break.	Values are given after a definite break.	Values are in the form of groups.

Array: 5,9, 10, 12, 14, 15, 15, 16, 17, 18, 18, 19, 20, 22,23, 24, 25, 27, 29.

Following steps are followed to convert an exclusive series into an inclusive series.

1. Find the difference between upper limit of preceding class and lower limit of succeeding class.
2. Divide this difference by 2.
3. Add this number in upper limit of all classes and deduct this number from lower limit of all classes.

For example, if classes are 0 - 9,10 - 19, 20 29 and so on. Then the difference between upper limit and lower limit of two succeeding classes is one. When we divide it by 2, we get 0.5. Therefore on deducting this number from upper limit and adding this number in lower limit, we can get new class intervals as- (-) 0.5 -9.5, 9.5 - 19.5, 19.5 and so on.

There is an inherent shortcoming in the classified data. No matter classification of data summarises the raw data by making it concise and easy to comprehend. But it does not show the details found in the raw data. There is thus a loss of information in classifying raw data. On the other hand, much is gained by summarising it as a classified data.
Once the data are grouped into classes, an individual value has no significance in further statistical calculations. Thus, the use of class mark instead of the actual value of the observation in statistics involves indeed, a considerable loss of information.

Univariate Frequency Distribution	Bivariate Frequency Distribution
The word 'Uni' refers to one.	The word 'Bi' refers to two.
This implies a series of statistical information representing the frequency distribution of one variable.	This implies a series of statistical information representing the frequency distribution of two variables such as production and sales of a particular product.
Examples: Marks of a Class VI student, income of an individual in a particular area.	Example: Production and sales of a particular product.

A characteristic, number, or quantity whose value changes overtime is called variable.
For example: Weight, income etc. It can be either discrete or continuous.

Discrete Variable	Continuous Variable
A variable that takes only whole number as its value is called discrete variable.	A variable that can take any value, within a reasonable limit is called a continuous variable
These variables increase in jumps or in complete numbers.	These variables assume a range of values or increase in fractions and not in jumps
For example: Number of people in a family, number of students in a class, etc.	For example: age, height, weight, etc.

C.L.	f
0-10	16
10-20	24
20-30	30
30-40	18
40-5	8
50-60	4

1. Height of a student is a continuous variable. It is so because it can take fractional values like 80.85 cm, 101.62 cm etc.
2. Distance covered is a continuous variable. It is so because it can take fractional values like 48.4 km, 59.2 km etc.
3. Number of students in a class is a discrete variable because it can take value of whole numbers only. It cannot take fractional values, e.g., number of students can be 40 or 41 but not 40.5 or 40.6.