Semester I-mb0040-statistics For Managers.doc

ASSIGNMENT Note –Answer all questions. Kindly note that answers for 10 marks questions should be approximately of 400 words. Each question is followed by evaluation scheme. 1

Explain the concept of inferential statistics and how it is different from Descriptive statistics

Answer: Inferential statistics Inferential Statistics is used to make valid inferences from the data for effective decision making among managers or professionals. Statistical methods such as estimation, prediction and hypothesis testing come under inferential statistics. The researchers make deductions or conclusions, regarding some characteristics of a population from the data that is collected from a sample of that population. Inferential Statistics means making inference, hypothesis testing, determining relationships and making predictions. Inferential statistics is the process of using data obtained from a sample to make estimates about the characteristics of a population. Inferential statistics deals with reaching valid conclusions about the data in order to make effective judgment. Inferential Statistics is used to make valid inferences from the data for effective decision making among managers or professionals. Difference between Inferential statistics Descriptive statistics Descriptive Statistics is used to present the general description of data which is summarised quantitatively. This is mostly useful in clinical research, while communicating the results of experiments while Inferential Statistics is used to make valid inferences from the data for effective decision making among managers or professionals. Descriptive Statistics gives the general description of quantitative data, whereas inferential statistics deals with reaching valid conclusions about the data in order to make effective judgment. Descriptive statistics is tabular, graphical and numerical methods used to summarise data while inferential statistics is the process of using data obtained from a sample to make estimates about the characteristics of a population. Descriptive Statistics means Collecting, Organising, Summarising and Presenting data whereas Inferential Statistics means Making inference, Hypothesis testing, Determining relationships and Making predictions. 2

Find out mean and median of following data.

Class interval Frequency

510 5

1015 4

1520 12

2025 14

2530 19

3035 17

3540 21

4045 8

Answer: Computation of Mean: Class interval 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50

Frequency (f) 5 4 12 14 19 17 21 8 16

Mid point (m) 7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5

fm 37.5 50 210 315 522.5 552.5 787.5 340 760

4550 16

N=116

Σfm = 3575

Mean: 3575/116=30.82

Computation of Median: Class interval 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50

Frequency 5 4 12 14 19 17 21 8 16 N=116

Less than Cumulative frequency LCF 5 9 21 35 54 71 92 100 116

N/2 =116/2 = 58 Cum. frequency just above 58 is 71 and hence, 30 – 35 is median class. Median = l+h/f [N/2 – c.f] Where, l = Lower limit of median class = 30. c.f = Cumulative frequency of class preceding the median class = 54 f = frequency of median class = 17 h = class width = 5 l=30 h=35-30=5 f=17 c.f=54 Median = 30+5/17 [116/2 - 17] =42.06

3 List out various Characteristics of Business Forecasting. Also, e l a b o r a t e t h e forecasting process. Answer: Characteristics of Business Forecasting: 1. Based on past and present conditions Business forecasting is based on past and present economic condition of the business. To forecast the future, various data, information and facts concerning to economic condition of business for past and present are analysed. 2. Based on mathematical and statistical methods The process of forecasting includes the use of statistical and mathematical methods. By using these methods, the actual trend which may take place in future can be forecasted. 3. Period The forecasting can be made for long term, short term, medium term or any specific period. 4. Estimation of future Business forecasting is to forecast the future regarding probable economic conditions. 5. Scope Forecasting can be physical as well as financial.

Forecasting process: Forecasting of business fluctuations consists of the following steps: 1. Understanding why changes in the past have occurred One of the basic principles of statistical forecasting is that the forecaster should use past performance data. The current rate and changes in the rate constitute the basis of forecasting. Once they are known, various mathematical techniques can develop projections from them. If an attempt is made to forecast business fluctuations without understanding why past changes have taken place, the forecast will be purely mechanical. Business fluctuations are based solely upon the application of mathematical formulae and are subject to serious error. 2. Determining which phases of business activity must be measured After understanding the reasons of occurrence of business fluctuations, it is necessary to measure certain phases of business activity in order to predict what changes will probably follow the present level of activity. 3. Selecting and compiling data to be used as measuring devices There is an independent relationship between the selection of statistical data and determination of why business fluctuations occur. Statistical data cannot be collected and analysed in an intelligent manner unless there is sufficient understanding of business fluctuations. It is important that reasons for business fluctuations be stated in such a manner that it is possible to secure data that is related to the reasons. 4. Analysing the data Lastly, the data is analysed to understanding the reason why change occurs. For example, if it is reasoned that a certain combination of forces will result in a given change, the statistical part of the problem is to measure these forces, from the data available, to draw conclusions on the future course of action. The methods of drawing conclusions may be called forecasting techniques.

4

Elaborate the concept of Range. Salary distribution of any manufacturing unit is given below Income in 1000

5 - 10

10- 15

15-20

20-25

25-30

No of Employees

4

3

7

9

4

Calculate the mean salary and standard deviation. Answer Concept of Range:‘Range’ represents the differences between the values of the extremes. The range of any sample is the difference between the highest and the lowest values in the series. The values in between two extremes are not taken into consideration. The range is a simple indicator of the variability of a set of observations. It is denoted by ‘R’. In a frequency distribution, the range is taken to be the difference between the lower limit of the class at the lower extreme of the distribution and the upper limit of the class at the upper extreme of the distribution. Range can be computed using following equation. Range = Largest value – Smallest value = L – S

Calculation of Mean salary:Class interval Income in 1000

Frequency (f) No of Employees

Mid point (m)

fm

Fx2 (1000000)

5-10 10-15 15-20 20-25 25-30

4 3 7 9 4

7.5 12.5 17.5 22.5 27.5

30 37.5 122.5 202.5 110 Σfm = 502.5

225 468.75 2143.75 4556.25 3025 10418.75

N=27 Mean salary = 502.5/27=18.61 =18610 Calculation of Standard deviation:Mean= 18610

SD= (10418750000/27-18610*18610) SD= 39547529.62 5

Briefly explain the Regression analysis. How it is different from Correlation?

Answer: According to M. M. Blair, Regression is defined as, “the measure of the average relationship between two or more variables in terms of the original units of the data”. Regression analysis is used to estimate the values of the dependent variables from the values of the independent variables. Regression analysis is used to get a measure of the error involved while using the regression line as a basis for estimation. The regression coefficient Y on X is the coefficient of the variable ‘X’ in the line of regression Y on X. Regression coefficients are used to calculate the correlation coefficient. The square of correlation is the product of regression coefficients. Regression lines For a set of paired observations, there exist two straight lines. The line drawn in such a way that the sum of vertical deviation is zero and the sum of their squares is minimum, is called regression line of ‘Y’ on ‘X’. It is used to estimate ‘Y’ values for given ‘X’ values. The line drawn in such a way that the sum of horizontal deviation is zero and sum of their squares is minimum, is called regression line of ‘X’ on ‘Y’. It is used to estimate the ‘X’ values for the given ‘Y’ values. The smaller the angle between these lines, the higher is the correlation between the variables. The regression lines always intersect at ( X Y )

Difference between Regression & Correlation analysis: Correlation Coefficient The correlation coefficients, rxy = ryx ‘r’ lies between -1 and 1. It has no units attached to it. There exists nonsense correlation. It is not based on cause and effect relationship. It indirectly helps in estimation.

Regression Coefficient The regression coefficients, byxbxy ‘byx’ can be greater than one in which case ‘bxy’ must be less than one such that byx.bxy1 It has units attached to it. There is no such nonsense regression. It is based on cause and effect relationship. It is meant for estimation.

6. Write a short note on following: i. Long term trend or secular trend ii. Seasonal variations iii. Cyclic variations iv. Random variations Answer: i) Long term trend or secular trend This refers to the smooth or regular long term growth or decline of the series. This movement can be characterised by a trend curve. If this curve is a straight line, then it is called a trend line. If the variable increases over a long period of time, then it is called an upward trend. If the variable decreases over a long period of time, then it is called a downward trend. If the variable moves upward or downward along a straight line then the trend is called a linear trend, otherwise it is called a non-linear trend.

ii) Seasonal variations Variations in a time series that are periodic in nature and occur regularly over short periods of time during a year are called seasonal variations. These variations are precise and can be forecasted. The following are examples of seasonal variations in a time series. 1. The prices of vegetables drop down after rainy season or in winter months and they go up during summer, every year. 2. The prices of cooking oils reduce after the harvesting of oil seeds and go up after some time. iii) Cyclic variations The long-term oscillations that represent consistent rise and decline in the values of the variable are called cyclic variations. Since these are long-term oscillations in the time series, the period of oscillation is usually greater than one year. The oscillations are either a trend curve or a trend line. The period of one cycle is the time-distance between two successive peaks or two successive troughs. iv) Random variations Random variations are called irregular movements. Movements that occur usually in brief periods of time, without any pattern and which are unpredictable in nature are called irregular movements. These movements do not have any regular period or time of occurrences. For example, the effect of national strikes, floods, earthquakes, etc. It is very difficult to study the behaviour of such a time series.