MB0040 – Statistics For Management - SET 1 - F

8/6/2019 MB0040 Statistics For Management - SET 1 - F

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Master of Business Administration- MBA Semester 1

MB0040 STATISTICS FOR MANAGEMENT

(Book ID: B1129)

Assignment Set- 1

Name : CHERUKURI ASOK KUMAR

Registration / Roll No. : 521058426

1. Why it is necessary to summarise data? Explain the approaches available to summarize the

data distributions?

Answer:

Graphical representation is a good way to represent summarized data. However, graphs provide usonly an overview and thus may not be used for further analysis. Hence, we use summary statistics likecomputing averages. To analyse the data. Mass data, which is collected, classified, tabulated andpresented systematically, is analysed further to bring its size to a single representative figure. Thissingle figure is the measure which can be found at central part of the range of all values. It is the one

which represents the entire data set. Hence, this is called the measure of central tendency.

In other words, the tendency of data to cluster around a figure which is in central location is known as

central tendency. Measure of central tendency or average of first order describes the concentration oflarge numbers around a particular value. It is a single value which represents all units.Statistical Avera ges: The commonly used statistical averages are arithmetic mean, geometricmean, harmonic mean.

Arithmetic mea n is defined as the sum of all values divided by number of values and is representedbyX .Before we study how to compute arithmetic mean, we have to be familiar with the terms such asdiscrete data, frequency and frequency distribution, which are used in this unit.If the number of values is finite, then the data is said to be discrete data. The number of occurrencesof each value of the data set is called frequency of that value. A systematic presentation of the valuestaken by variable together with corresponding frequencies is called a frequency distribution of the

variable.

Median: Median of a set of values is the value which is the middle most value when they arearranged in the ascending order of magnitude. Median is denoted by M.

Mode: Mode is the value which has the highest frequency and is denoted by Z .Modal value is most useful for business people. For example, shoe and readymade garmentmanufacturers will like to know the modal size of the people to plan their operations. For discretedata with or without frequency, it is that value corresponding to highest frequency.


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Appr opr iat e Situ at i ons for the use of Var ious Aver ages:

1. Ar i thm eti c mean i s used w hen:a. In depth study of the variable is needed

b. The variable is continuous and additive in naturec. The data are in the interval or ratio scaled. When the distribution is symmetrical

2. Median is used w hen:a. The variable is discrete

b. There exists an abnormal valuec. The distribution is skewedd. The extreme values are missinge. The characteristics studied are qualitativef. The data are on the ordinal scale

3. M ode is used w hen:a. The variable is discrete

b. There exists an abnormal value

c. The distribution is skewedd. The extreme values are missinge. The characteristics studied are qualitative

4. Geometr ic m ean is used w hen:a. The rate of growth, ratios and percentages are to be studied

b. The variable is of multiplicative nature5. Harmonic mean is used when:a. The study is related to speed, time

b. Average of rates which produce equal effects has to be found

5 Positional Averages

Median is the mid-value of series of data. It divides the distribution into two equal portions. Similarly,we can divide a given distribution into four, ten or hundred or any other number of equal portions.

2. Explain the purpose of tabular presentation of statistical data. Draft a form of tabulation to

show the distribution of population according to i) Community by age, ii) Literacy , iii) sex , and

iv) marital status.

Answer:

Tabulation is an orderly arrangement of data in columns and rows systematically in a tabular form. Itis the logical listing of related quantitative data in vertical columns and horizontal rows. The

presentation of data in tables should be simple, systematic and unambiguous.

The purpose of tabular presentation of statistical data is to:

a) Simplify complex d ata: Tabulation simplifies the complex data by presenting themsystematically in columns and rows in a condensed form. It avoids all the unnecessary data that isfound in a narrative form.


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b) Highlight importan t characteristics: It also helps to highlight the important characteristicsof the data. As it avoids all the unnecessary data that is usually found in a narrative form.

c) Present data in minimu m space: Tabulation achieves economy in using the space forpresenting the data. The textual matter is presented neatly in a short form without sacrificing utility ofthe data.

d) Facilitate compar ison: The data presented in a tabular form is helpful for a comparative study.

The relationship among the various items can be easily understood.

e) Bring out trends and tendencies: Tabulation depicts the data and their significance at first inthe form of figures, which cannot be understood when the same data are in a narrative form.

f) Facilitate further analysis: The Tabulation is analytical in nature and hence it helps in furtheranalysis.

Marital Status Sex Educated Non-EducatedAge Below

20Yrs20to40

Above40

Below20Yrs

20to40

Above40

Married MaleFemale

Un Married MaleFemale

3. Give a brief note of the measures of central tendency together with their merits & Demerits.

Which is the best measure of central tendency and why?

Answer:

Graphical representation is a good way to represent summarized data. However, graphs provide usonly an overview and thus may not be used for further analysis. Hence, we use summary statistics likecomputing averages. To analyse the data. Mass data, which is collected, classified, tabulated andpresented systematically, is analyzed further to bring its size to a single representative figure. Thissingle figure is the measure which can be found at central part of the range of all values. It is the one

which represents the entire data set. Hence, this is called the measure of central tendency.

In other words, the tendency of data to cluster around a figure which is in central location is known ascentral tendency. Measure of central tendency or average of first order describes the concentration oflarge numbers around a particular value. It is a single value which represents all units.

Arithmetic mean: Arithmetic mean is defined as the sum of all values divided by number of valuesand is represented by

Merits and Demerits of arithmetic mean

Merits DemeritsIt is simple to calculate and easy to understand. It is affected by extreme values.It is based on all values It cannot be determined for distributions with

open-end class intervals.


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It is rigidly defined. It cannot be graphically located.It is more stable. Sometimes it is a value which is not in the series.It is capable of further algebraic treatment.

Median: Median of a set of values is the value which is the middle most value when they arearranged in the ascending order of magnitude. Median is denoted by M

Merits and Demerits of median

Merits DemeritsIt can be easily understood and computed. It is not based on all values.It is not affected by extreme values. It is not capable of further algebraic treatment.It can be determined graphically (Ogives). It is not based on all values.It can be used for qualitative data.It can be calculated for distributions with open-end classes.

Mode: Mode is the value which has the highest frequency and is denoted by Z.Modal value is most useful for business people. For example, shoe and readymade garment

manufacturers will like to know the modal size of the people to plan their operations. For discretedata with or without frequency, it is that value corresponding to highest frequency.

Merits and Demerits of mod e

Merits Demerits

In many cases it can be found byinspection.

It is not based on all values.

It is not affected by extreme values. It is not capable of furthermathematical treatment.

It can be calculated for distributionswith open end classes.

It is much affected by samplingfluctuations.

It can be located graphically.It can be used for qualitative data.

The best measure of tendency is arithmetic mean. It is defined as a value obtained by dividing the sumof all the observation by their number, that is mean= [sum of all the observations]/ [number of theobservations] Arithmetic mean is used because it is simple to understand and easy to interpret. It isquickly and easily calculated. It is amenable to mathematical treatments. It is relatively stable inrepeated sampling experiments.


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So Z-test statistics will be used for hypothesis testing.

Let us take the null hypothesis, H0Let mean weight has increasedH1 and HA for alternate hypothesis

H0 : = 5

H1 : > 5 ( Right Tailed test )

Given, Sample size = n = 100

Mean Weight = = 5.03 kg

Standard deviation = S = 0.21 kgLevel of significance, = 5%

Z = ( - ) / (S / n)

= (5.03 5 ) / (0.21 /100)

Z calculated = 1.428

Now, check the table for 5%Now, Z critical = Z= Z0.05 = 1.645 ( For one tailed test )

Since calculated value, Z calculated = 1.428 is less than its critical value Z = 1.645

Therefore, H0 is accepted.

Hence we conclude the mean weight produced by the machine has increased.

6. Find the probability that at most 5 defective bolts will be found in a box of 200 bolts if it is

known that 2 per cent of such bolts are expected to be defective .(you may take the distribution

to be Poisson; e-4= 0.0183).

Answer:

Given, total number of bolts, n = 200

P (defective bolt) = 2% = 0.02Therefore, m = np = 200 * 0.02 = 4

P(X = 0) = P (zero defective bolt)

= (e-m

m0

) / 0!

= (e-4

40) / 1

= ( 0.0183 ) ( 1 ) / 1


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= 0.0183=========

P ( at most 5 defective bolts )

= P (X5)

= P (X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

= (e-m

m0) / 0! + (e

-mm

1) / 1! + ( e

-mm

2) / 2! + ( e

-mm

3) / 3! + (e

-mm

4) / 4! + (e

-mm

5) / 5!

= e-m

[ 1 + m1

/ 1! + m2 /2! + m

3 /3! + m

4 /4! + m

5/5! ]

= e-4

[1 + 41

/ 1 + 8/2 + 64/6 + 256/24 + 1024/120 ]

= 0.0183 [ 1 + 4 + 8 + 10.67 + 10.67 + 8.53 ]

= 0.0183 * 42.87

= 0.784521

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MB0040 – Statistics For Management - SET 1 - F