Economics 6 Marks Question

Less Than' Cumulative Frequency Distribution.

Wages (In ₹)	Cumulative Frequency(cf)
Less than 110	4
Less than 120	16
Less than 130	36
Less than 140	43
Less than 150	48

‘More Than' Cumulative Frequency Distribution.

Wages (In ₹)	Cumulative Frequency (cf)
More than 100	48
More than 110	44
More than 120	32
Morte han 130	12
More than 140	5

1. (b) False

Explanation:

Times series graphs are based upon the data given over different time period and not on the basis of general characteristics.

2. (d) Both (a) and (b)

3. (a) Qualitative

4. (a) Continuous exclusive frequency distribution.

The frequency array of cell phones used by 45 families is as follows:

Thus from the above frequency array we can conclude that, out of 45 families, one family is not using any cell phone, 7 families are using 1 cell phone, 15 families are using 2 cell phones, 12 families are using 3 cell phones, 5 families are using 4 cell phones, 2 families are using 5 cell phones, 2 are using 6 cell phones and only 1 family is using 7 cell phones.

There are two methods of classifying data into class intervals.

1. Exclusive method: Under this method the upper limits of one class is the lower limits of the next class. In this way continuity of the data is maintained. E.g. class intervals are 0-5, 5-10, 10-15 and so Now 5 is coming twice so is 10 and 15. So the upper limit of the class is excluded, means if a student has obtained 5 marks he is not included in the first group i.e. 0-5, but in the second i.e. 5-10.
2. Inclusive method: Under this method upper limits of the class interval are also included in that class. The class interval will be made like 0-4, 5-9, 10-14 and so 0 This does not exclude the upper class limit in a class interval. Both class limits upper and lower limits are parts of the class interval.

1. (a) Spatial classification

Explanation:
As the data is classified based upon the geographical area, it is known as geographical classification or spatial classification.

2. (a) Inclusive

Explanation:
In an inclusive series, the upper limit of the first class is not equal to the lower limit of the succeeding class.

3. (c) Unequal and inclusive

Explanation:
The given series is inclusive as well as unequal as the class interval/width are not same for all classes.

4. (d) All of the above

5. (d) None of these

Explanation:
In the given case, 19.5 can only be recorded once the series is converted into an exclusive series.

Generally, data are classified on the basis of the following four bases: Geographical Classification: In geographical classification, data are classified on the basis of geographical or locational differences – such as cities, districts, or villages – between various elements of the data set. The following is an example of a geographical distribution. (Figures are hypothetical)

States of India	Punjab	Haryana	J & k	Bihar	Orissa	M.P.
Poverty (%)	12	10	3.5	39	38	34

Chronological Classification: When data are classified on the basis of time, the classification is known as chronological classification. Such classifications are also called time series because data are usually listed in chronological order starting with the earliest period. The following is an example of a Chronological distribution. (Figures are hypothetical)

Year	1951	1961	1971	1981	1991	2001
Poverty (%)	52	50	47	38	36	26

Another example can be:

Month	Family expenditure per member
January	2000
February	3000
March	1000
April	1200
May	2300
June	1400
July	1100
August	4300
September	900
October	1900
November	2100
December	3100

Qualitative Classification: In qualitative classification, data are classified on the basis of descriptive characteristics or on the basis of attributes like sex, literacy, region, caste, or education, which cannot be quantified. This is done in two ways: Simple classification: In this type of classification, each class is subdivided into two sub-classes and only one attribute is studied, for example male and female; blind and not blind, educated and uneducated; and so on. Manifold classification: In this type of classification, a class is subdivided into more than two subclasses which may be sub-divided further. An example is given below:
Quantitative Classification: In this classification, data are classified on the basis of characteristics which can be measured such as height, weight, income, expenditure, production, or sales. An example is given below:

Salary Per Month	No. of workers
0-10000	40
10,000-20,000	10
20000-30000	13
30000-40000	8
40,000-50,000	12
50,000 and above	7

3. Reducing bulk data and facilitating comparison.

According to Horace Secrist, "A series as used statistically may be defined as things or attributes of things arranged according to some logical order." According to Prof. Connor, "If two variable quantities can be arranged side by side so that measurable difference in the one corresponds with measurable difference in the other, the result is said to form a statistical series." On the Basis of Characteristics:

1. Time Series: When series of values of some variable which is represented according to successive points in time is called time series. In such a series, data are represented with reference to a time period which can be a year, week, month or day. An example is given below:

Production in a cloth mill:

Year	2005	2006	2007	2008	2009	2010
Production (in 000 meters)	15	27	58	72	134	140

OR
Rainfall in a week

DAY	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Rainfall in cm	15	27	17	14	54	64	10

2. Spatial Series: A series of values of some variable which is represented according to area under investigation i.e. geographical division of the universe is called spatial series. An example is given below:

Production of wheat in different states of India in 2010

States	Punjab	Haryana	Maharashtra	U.P.	Bihar	Orissa
Production (in 000 tonnes)	1500	2700	580	720	134	140

3. Condition Series: A series of values of some variables which is represented according to condition which may be expressed in quantitative terms is called condition series. An example is given below:

	Grade
	A	B	C	Total
Boys	13	25	11	49
Girls	7	20	6	33
Total	20	45	17	82

A characteristic or phenomenon which,is capable of being measured and changes its value from time to time, place to place or situation to situation is called a variable. In other words, anything which is subject to change in value and can be measured is called a variable. Variable means "which varies". It may vary over time, person to person, place to place etc. for example, Income is a variable as it varies person to person (different people earn different incomes), place to place (salaries vary in India and America) and over time (salaries in 1951 were different from salaries in 2001). Temperature is a variable. It changes over time and also place to place. Height is a variable as it varies person to person and over time.
There are two types of Variable:
Discrete and Continuous
Discrete Variable: A discrete variable is one which increases in jumps or in complete numbers. For example, there can't be 2.4 workers in a factory. They can be 1, 2, 3, 4 and so on. Similarly, a factory can't have 4.8 or 2/7 machines. It will be in complete numbers like 1,2,3,4, and soon. Such variable are called discrete variable. Some other examples of discrete variable are number of workers in a factory, number of machines purchased, number of children etc.
Continuous Variable: Those variables which can assume any value in a given range and which increase continuously and not in jumps are called continuous variable. For example, weight of a person can be 45.234 kg, it can take any value within a range. No one gains weight in jumps. It increases in continuity. Other examples are height, income etc.

1. Range =176 – 119 = 57

2. The frequency distribution by dividing into appropriate classes is shown below.

3. Number of students whose weight is weight is.

1. less than 145 kg = 17 (12 + 4 +1)
2. more than 155 kg = 9 (5 + 3 + 1)
3. between 135 and 155 kg = 26 (12 + 14)

To understand these terms we are taking two series for reference one is discrete frequency distribution and second is continuous frequency distribution. Series-1 Discrete Frequency Distribution

Shoe Size	7	8	9	10	11	12
No of students	8	12	20	10	6	4

Series 2 Continuous Frequency Distribution

Marks	0-10	10-20	20-30	30-40	40-50	50-60
No of students	8	12	20	10	6	4

1. Frequency: Frequency is the number of times a value repeats itself in the observations. For example when we have written 8 before 7 in series 1, it means 8 students have a shoe size of 7 number in raw data. 12 students have got 8 size, 20 got 9 size and so on. It is applicable to discrete frequency distribution
2. Class Frequency: Frequency of a class instead of specific observation is called class frequency. It shows how many items have a value in that class interval. For example, when we have written 10 in column of number of students in front of 30-40, it means 10 students have got marks equal to or more than 30 but less than 40.
3. Class: It refers to decided group of magnitudes. For example, 0-10 in series 2. It may be 0-9, 10-19 or 4.5 – 8.5 and so on.
4. Upper and Lower limits of the Class: Lower limit is the lower magnitude of the class and upper limit is the upper magnitude of class. For example in class 0-10, 10 is the lower limit and 10 is the upper limit.
5. Total Frequency: It is the sum total of frequencies of all classes. It must be equal to total number of observations.
6. Frequency Distribution: When observations are distributed over several values, it is termed as frequency distribution. For example, in above examples, I series is an example of discrete frequency distribution of shoe El size of students. Series 2 is a continuous 2 frequency distribution of marks obtained TREI by students.
7. Class Interval: Class Interval refers to the magnitude spread between the lower and upper class limit. In other words, it is span or width of the class. It can be obtained by deducting lower limit from upper limit. It is applicable to continuous series only. In series two, class interval is 10 (10-0=10) for first class and for other classes as well. But it is not necessary that all classes should have same class interval. Depending on the purpose, unequal class intervals for different classes can also be used. For example:

Pocket Expenses Frequency	Frequency
0-10	2
10-30	9
30-100	3
100-500	5
500-1000	4
1000-2000	2

8. Mid Value: It is the average of lower limit and upper limit. It can be obtained by dividing the sum of lower limit and upper limit by 2. For example, in series 2 given above, we can find mid values as follows:

Daily Income	No of families	Mid Value
0-100	5	50
100-200	9	150
200-300	12	250
300-400	2	350
500-600	2	450

1. Discrete Series: A series which See represents a discrete variable is called discrete series. For example, series -1 of shoe size is a discrete series.
2. Continuous Series: A series which represents continuous variable is called a continuous series. For example, in series 2, the distribution of marks amongst students is a continuous series.

Table 3.2
Monthly Household Expenditure (in Rupees) on Food of 50 Households

1904	1559	3473	1735	2760
2041	1621	1753	1855	4439
5090	1085	1823	2346	1523
1211	1360	1110	2152	1183
1218	1315	1105	2628	2712
4248	1812	1264	1183	1171
1007	1180	1953	1137	2048
2025	1583	1324	2621	3676
1397	1832	1962	2177	2575
1293	1365	1146	3222	1396

1. Calculation of Range:

Range = Highest Value - Lowest Value
Highest Value = 5090
Lowest Value = 1007
So, Range = 5090 - 1007 = 4083

2. Frequency distribution of expenditure: Given that the lowest monthly household expenditure is 1007 and the highest monthly household expenditure is 5090. The distribution of frequencies will relate to values between 1000 and 5500. Thus, the class interval will be 500.

3.  

1. Number of households whose monthly expenditure on food is less than ₹ 2000

= 20 + 13 = 33

2. Number of households whose monthly expenditure on food is more than ₹ 3000

= 2 + 1 + 2 + 0 + 1 = 6

3. Number of households whose monthly expenditure on food is between ₹ 1500 and ₹ 2500

= 13 + 6 = 19

When we group data in a continuous series as shown below, we get to know
only the fact that 4 students have marks more than equal to or more than 0 and o less than 10 but we do not know the exact figures.

Marks	Frequency
0-10	4
10-20	7
20-30	4
30-40	3
40-50	2

Suppose all 4 had 1 mark, they will be in class 0-10 and even when all 4 have 9 marks, they will be in class0-10. It is called loss of information in organized data.