MB0040 & STATISTICS FOR MANAGEMENT

Q-1Distinguish between Classification and Tabulation. Explain the structure andcomponents of a Table with an example.

Ans-1 Meaning of Classification: According to Secrist, Classification is the process of arranging data into sequences and groups according to their common characteristics or separating them into different but related parts.According to Stockton and Clark, The process of grouping large number of individual facts and observations, on the basis of similarity among the items is called Classification.

Tabulation: Tabulation follows classification. It is a logical or systematic listing of relateddata in rows and columns. The row of a table represents the horizontal arrangement of data and column represents the vertical arrangement of data. The presentation of data in tables should be simple, systematic and unambiguous.

Basic differences between Classification and Tabulation

ClassificationTabulation

It is the basis for tabulationIt is the basis for further analysis

It is the basis for simplificationIt is the basis for presentation

Data is divided into groups and subgroups on the basis of similaritiesand dissimilarities.Data is listed according to a logicalsequence of related characteristics

Structure and Components of a Table with an example

Tab 1: Table numberTable number is to identify the table for reference. When there are many tables in an analysis, then table numbers are helpful in identifying the tables.

Tab 2: TitleTitle indicates the scope and the nature of contents in a concise form. In other words, title of a table gives information about the data contained in the body of the table. Title should not be lengthy.

Tab 3 and Tab 4: CaptionsCaptions are the headings and subheadings describing the data present in the columns.

Tab 5 and Tab 6: StubsStubs are the headings and subheadings of rows.

Tab 7: Body of the tableBody of the table contains numerical information.

Tab 8: TotalsThe sub-totals for each separate classification and a general total for all combined classes should be given at the bottom or right side of the figures whose totals are taken. Ruling and spacing separate columns and rows. However, totals are separated from main body by thick lines.

Tab 9: Head noteHead note is given below the title of the table to indicate the units of measurement of the data and is enclosed in brackets.

Tab 10: Source noteSource note indicates the source from which data is taken. The source note related to table is placed at the bottom on the left hand corner.

Q-2 (a) Explain Arithmetic mean.(b) The mean wage is Rs. 75 per day, SD wage is Rs. 5 per day for a group of 1000workers and the same is Rs. 60 and Rs. 4.5 for the other group of 1500 workers.Find the mean and standard deviation for the entire group.

Ans-2 (a) Arithmetic meanArithmetic mean is defined as the sum of all values divided by number of values and is represented by X . Arithmetic mean is also called average. It is most commonly used measures of central tendency. Arithmetic Mean of a series is the value obtained by adding all the observations of a series and dividing this total by the number of observations.

There are two types of Arithmetic Mean:a. Simple arithmetic Meanb. Weighted arithmetic Mean

Simple arithmetic MeanArithmetic mean is simply sometimes referred as Mean. For example: mean income, mean expenses, mean marks, etc.Simple Arithmetic Mean is equal to the sum of the values of the variabledivided by their number of observations.

Weighted arithmetic meanThe weighted mean is computed by considering the relative importance of each of the values to the total value. The arithmetic mean gives equal importance to all the items of distribution. In certain cases, relative importance of items is not the same. To give relative importance, weight age may be given to variables depending on cases.

(b) Solution: We have by data, 1 = 75, 1 = 5, N1 = 1000

2 = 60, 2 = 4.5, N2 = 1500

Q-3 Mr. Arun and Mr. Bhandari play a game. If Mr. Arun picks up an even number from1 to 6, Mr. Bhandari will pay him double the amount equal to picked up number. IfMr. Arun picks up an odd number then he has to pay amount equal to double thepicked up number. What is Mr. Aruns expectation?

Ans-3 SolutionLet Xi be the random variable and P(Xi) be its probability. The probabilities are indicated in table

Table: Required Values for Calculating Mean and Variance for the Data

NO.(Xi)(Xi)Xi P(Xi)

1.-21\6-2/6

2.41\64/6

3.-61\6-1

4.81\68/6

5.-101\6-10/6

6.121\6-12/6

Total11

Expectation of Mr. Arun is E= i=1.

Q-4 The probability that an employee will get an occupational disease is 20%. In a firm having five employees, what is the probability that:i) None of the employees get the diseaseii) Exactly two will get the diseaseiii) More than four will contract the diseaseAns-4 SolutionGiven thatp=q 10.2 0.8 n = 5Therefore, by binomial distribution, P 5-x xx x 5C (0.8) (0.2)