SUBMITTED TO MRS VIKRAM KAUR SUBMITTED BY KUNAL

SUBMITTED TO : MRS. VIKRAM KAUR SUBMITTED BY: KUNAL AGGARWAL (190) BCOM 1 -B

Ans. Ans A= Rs. 12000 r= 12. 5% n= 5 years A= 12000= p × 12000= p= p= Rs. 6659 (approx. )

Ans- Various formulas can be used for the construction of index number. Prof. Fisher has given the following test to select an appropriate formula: (1)Time Reversal Test (TRT) (2)Factor Reversal Test (FRT) (3) Circular Test (1) Time Reversal Test - The test is that fprmula for calculating an index number should be such that it will give the same ratio between one point of comparison and the other, no matter which of the two is taken as base. × = =1

� (2)Factor Reversal Test – Just as our formula should permit the interchange of two items without givimg inconsisting results , so it ought to permit interchange of prices and quantities without giving inconsistent results I. e the two results multiplied together shoul give the true value ratio. = � (3) Circular Test : Index number based on simple G. M simple aggregative formula and weighted aggregative formula ( with fixed weights ) satisfy circular test 1

Ans -EXHAUSTIVE EVENTS The total number of possible outcome of a experiment are called xhaustive events. In the other words , if all the possible outcomes of an experiment are taken into consideration , then such events are called exhaustive events Example*In case of tossing a die, the set of six possible outcomes i. e 1, 2, 3, 4, 5 and 6 are exhaustive events *In case of tossing a coin , the set of 2 outcomes , i. e 4 and 7 are exhaustive events *In case of tossing of two dice , the set of possible outcomes are 6*6 = 36 EQUALLY LIKELY EVENTS The events are said to be equally likely if the chance of happening of each event is equal or same. In other words , events are said to be likely when one doesn’t occur more often than others. Example*If a coin is tossed , the events H and T are equally likely events.

ANS: Number of exhaustive cases = n = 52 There are 4 aces cards in an oridinary pack. * Number of favourable cases =m=4 * Probability of getting an ace = 4/52 =1/13

� Ans- Binominal distribution is a discrete probability distribution. This distribution was discovered by a swiss mathematician JAMES BERNOULI. It is used in such situations where an experiment results in a two possibilities – success and failure. Binominal distrubition is a discrete probability distribution which expresses the probability of one set of two alternatives – success (p) and the failure(q) Binominal distribution is defined and given by the following probability function : = Where , p= probability of success q= probability of failure=1 -p n = no. of trails

Ans - Sampling methods is that method in which data is collected from sample of items selected from population and conclusion are drawn from them. Sampling techiniques has three main stages : (1) To select a sample (2) To collect information from it (3)To make inference regarding the population IMPORTANCE In modern times sampling method is an impotant and popular methods of statical inquiry. Besides economic and business world, this method is widely used in daily life. For example- A housewife comes to know of cooking the whole lot of ric by observing two-three grains only

MERITS (1) It is less expensive (2)Data can be collected more quickly (3) A no. of items is less so they can be intensively studied DEMERITS (1)These methods have less accuracy (2) There are wrong calculations (3)Ths is a complex method as specialsed knowledge is required to select a sample

�Ans. - The following are some of the difficulties of measuring national income I india: � � � ( 1) NON MONETISED SECTOR In the estimation of national income , it is assumed that the economy of the country is a monetized economy in which goods and services are exchanged for money. It becomes very difficult to find out the market value of production , further most of these producers in India donot keep accounts of their production and sale. (2) INCOMPLETE STATISTICS In India , data are incomplete as well as inreliable. Therefore , it becomes more difficult to make precise estimate of national income. (3) DIFFICULTY IN AVAILABILITY OF STATS Supply of data is very scare in india. It is particularly relating to agriculture and allied activities. The people in rural areas hardly give any information on consumption or saving.

� (4)INTER REGIONAL DIFFERENCE : There are different circumstances in different regions of the country. Accordingly , it becomes difficult to use data of one region from the another in extended form (5) MISCELLANEOUS DIFFICULTIES: These difficulties relate to administrative changes , illiteracy and lack of skilled of personal to collect information and prepare estimates.

� Firstly, dispersion refres to the variations of the items among themselves. If the value of all the items of a series is the same , there will be no variation among the various itms and trhe dispersion will be zero. Secondly, Dispersion refers to the variation of the items around an average. If the difference between the value of the items and average is small , the dispersion will be low. Thus , dispersion is defined as scatterness or spreadness of the individual items in a given series. OBJECTIVES OF MEASURING DISPERSION (1) To determine the reliability of an average: The measure of dispersion help in determining the reliability of an average. It points out as to how fr an average is representive of a statistical services.

(2) To determine the variability of two or ore series : The measure of dispersion helps in comparing the variability of two or more series. It is also useful to determine the uniformity or consistency of two or more series. � (3)For facilitating the use of other statistical measures: Measures of dispersion serves the basisi of many other statistical measures such as correlation, regression etc. These measures are based on measures of variation of one kind or another. � (4) Basis of statistical quality control: The measure of dispersion is the basis of statistical quality control. The extent of the dispersion gives indication to the management as to whether the variation in quality of the product is due to random factors or there is some defect in manufacturing process �

Ques. : From the following data construct chain base index numbers : Items 1999 2000 2001 2002 2003 X 5 8 10 12 15 Y 3 6 8 10 12 Z 2 3 5 7 10. 5 Ans. Table on next slide

ITEMS 1999 L. R 2000 L. R 2001 L. R 2002 L. R 2003 L. R X 5 100 8 160 10 12. 5 12 120 15 125 Y 4 100 6 200 8 133. 3 10 125 12 120 Z 3 100 3 150 5 166. 7 7 140 10. 5 150 TOTAL 30 510 425 395

YEARS AVERAGE CHAIN BASE INDEX 1999 300/3 = 100*100/100=100 2000 510/3 = 170*100/100=170 2001 425/3 =141. 7*170/100=240. 89 2002 385/3 = 128. 3*141. 7/100=181. 8 2003 395/3 = 131. 7*128. 3/100=168. 9

Ans. TIME SERIES- The set of data collected or observed on the basis of time (such as days , months, years) is called as time series. According to Kenny and keeping, ” a set of data depending on the time is called time series. ” COMPONENTS OF TIME SERIES � The four components of time series are: 1. Secular trend 2. Seasonal variation 3. Cyclical variation 4. Irregular variation

� Secular trend : A time series data may show upward trend or downward trend for a period of years and this may be due to factors like increase in population, change in technological progress , large scale shift in consumers demands, etc. For example, population increases over a period of time, price increases over a period of years, production of goods on the capital market of the country increases over a period of years. These are the examples of upward trend. The sales of a commodity may decrease over a period of time because of better products coming to the market. This is an example of declining trend or downward trend. The increase or decrease in the movements of a time series is called Secular trend. Seasonal variation: Seasonal variation are short-term fluctuation in a time series which occur periodically in a year. This continues to repeat year after year. The major factors that are responsible for the repetitive pattern of seasonal variations are weather conditions and customs of people. More woollen clothes are sold in winter than in the season of summer. Regardless of the trend we can observe that in each year more ice creams are sold in summer and very little in Winter season. The sales in the departmental stores are more during festive seasons that in the normal days.

� Cyclical variations(c): Cyclical variations are recurrent upward or downward movements in a time series but the period of cycle is greater than a year. Also these variations are not regular as seasonal variation. There are different types of cycles of varying in length and size. The ups and downs in business activities are the effects of cyclical variation. A business cycle showing these oscillatory movements has to pass through four phases-prosperity, recession, depression and recovery. In a business, these four phases are completed by passing one to another in this order. � Irregular variation-(I): Irregular variations are fluctuations in time series that are short in duration, erratic in nature and follow no regularity in the occurrence pattern. These variations are also referred to as residual variations since by definition they represent what is left out in a time series after trend , cyclical and seasonal variations. Irregular fluctuations results due to the occurrence of unforeseen events like floods, earthquakes, wars, famines, etc.

MARKS IN STATISTICS MARKS IN LAW 20 14 30 5 40 30 50 32 60 40 70 45 80 65

- ANS: y x RANK 1 RANK 2 R 1 - R 2 D 20 14 1 2 -1 1 30 5 2 1 1 1 40 30 3 3 0 0 50 32 4 4 0 0 60 40 5 5 0 0 70 45 6 6 0 0 80 65 7 7 0 0 = 1=1= = 0. 964

ANS: YEARS Y X XY 1997 38 -3. 5 133 12. 25 1998 40 -2. 5 100 6. 25 1999 65 -1. 5 97. 5 2. 25 2000 72 -0. 5 36 0. 25 2001 69 0. 5 34. 5 0. 25 2002 60 1. 5 30 2. 25 2003 87 2. 5 217. 5 6. 25 2004 95 3. 5 332. 5 12. 25

� Y=a a= +bx , b= a = 526/8 = 65. 75 , b = 981/42= 28. 36 y= a+bx =65. 75+ 23. 36 x Origin: y (2005) = 65. 75+ 23. 36 x = 65. 75+ 23. 36(4. 5) = 65. 75+105. 12 = 170. 87

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