Ppt Unit 04 Mbf103

C o n f i d e n t i a l1

Program : MBA

Semester : I

Subject Code : MBF103

Subject Name : Statistics for management

Book Code : B1129

Unit number : 4

Unit Title : Measures used to summarize Data.

Lecture Number : 6 ,7 & 8

Lecture Title : Central tendency

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C o n f i d e n t i a l

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Measures to summarize data

Objectives :

• Describe the concept of statistical average• Calculate arithmetic mean for discrete and continuous data• Calculate median and mode of data• Calculate quartiles, deciles and percentiles for the statistical data• Compute coefficient of variance for the statistical data

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Unit-4 Measures to summarize data


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Lecture Outline

• Introduction

• Central Tendency

• Requisites of Good Average

• Statistical Averages

• Merits & Demerits of Arithmetic mean

• Introduction to Median

• Introduction to Mode

• Geometric Mean

• Harmonic Mean

• Positional Averages

• Measures & Realative measures of Dispersion

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Lecture Outline

• Pre requisite for good measure of variation

• Range

• Quartile Deviations

• Other Measures

• Summary

• Check Your Learning

• Activity

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Introduction

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Graphical representation is a good way to represent summarised data. However, graphs provide us only an overview and thus may not be used for further analysis. Hence, we use summary statistics like computing averages to analyse the data. Mass data, which is collected, classified, tabulated and presented systematically, is analysed further to bring its size to a single representative figure.



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Centeral Tendency

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•Tendency of Data to Cluster around a Figure is called Central tendency

• Measures of Central Tendency or averages of first order describes the concentration of large numbers around a value.

• It is a single value representing all units

•This single 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.

www.visualstatistics.net/.../Contents.htm



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Requisites of Good Average

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It should be simple to calculate and easy to understand It should be based on all values It should not be affected by extreme values It should not be affected by sampling fluctuation It should be rigidly defined It should be capable of further algebraic treatment



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Statistical Averages

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The commonly used statistical averages are arithmetic mean, geometric mean, harmonic mean.

Arithmetic mean: Arithmetic mean is defined as the sum of all values divided by number of values and is represented by Before you study how to compute arithmetic mean, you have to be familiar with the terms such as discrete data, frequency and frequency distribution, which are used in this unit.

Properties of Arithmetic Mean1.Algebraic sum of deviations of a set of values taken from their Mean is always zero2.Sum of squares of deviations of a set of values from their mean is always minimum3.It is capable of further algebraic treatment



Merits and Demerits of Arithmetic Mean

MERITS DEMERITS

Simple to Calculate and Easy to Understand based on all values Rigidly Defined Capable of further algebraic treatment More Stable

Affected by extreme values Can not be determined for distributions with open-end class intervals Cannot be graphically located Sometimes it’s a value which is not in the series

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MEDIAN

MERITS DEMERITS

Can be easily understood & computed

Not affected by extreme values

Can be determined Graphically (ogives)

Can be used for Qualitative data

Can be calculated for distributions with open-end classes

Not based on all values

Not capable of further algebraic treatment


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Median is the Middle most value when they are arranged in the ascending

order of magnitude and is denoted by M.

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MODE

MERITS DEMERITS

Can be found by inspection in many cases

Not affected by extreme values

Can be located graphically Can be used for qualitative

data Can be calculated for

distributions with open end classes


Not capable of further mathematical treatment

Much affected by sampling fluctuations

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Mode is the value which has the highest frequency



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Geometric Mean

Geometric mean of a series of “n” positive numbers is given by –

Discrete series without frequency

Discrete series with frequency

Continuous Series

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nnXXXXGM .......... 321

n fn

ff nXXXGM ............. 2121

n fn

ff nXXXGM ........ 2121

X1, X2,…..,Xn are mid-points of class intervals



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Harmonic Mean

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If X1, X2,…..,Xn are “n” values for discrete series without frequency then their Harmonic Mean is

)/1(..

iX

NMH

For Discrete series with frequency

)/(..

ii Xf

NMH

Here, fi is the corresponding frequencies



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Positional Averages

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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.

For discrete series with or without frequency, Q1 and Q3 are given by: Q1 is (N+1/4)th value Q3 is [{3(n+1)}/4] value



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Measures of Dispersion

•Property of deviations of values from the average is called Dispersion or Variations.

Various Measures of Dispersion –1. Range (R)2. Quartile (Q.D.)3. Mean Deviations (M.D.)4. Standard Deviations (S.D.)



Relative Measures of Dispersion

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There are different relative measures of Dispersions:

Coefficient of Range Coefficient of Quartile Deviations Coefficient of Mean Deviations Coefficient of Variations

Prerequisite of Good Measure of Variation:

Should be easy to understand and simple to calculateShould be based in all valuesShould not be affected by extreme valuesShould not be affected by sampling fluctuationsShould be capable of further algebraic treatment



RANGE

MERITS DEMERITSEasily Understandable Simple to Calculate

Affected by Extreme values & not based on all values

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Difference between highest and lowest value of data iscalled as Range. i.e. R=H-L ; where H: Highest Value L: Lowest Value

Coefficient of Range = (H-L)/(H+L)

Uses of Range: Used in Statistical Quality control. When study does not require deep analysis and when data don’t have any abnormal values



Quartile Deviations

MERITS DEMERITS

Easily Understandable, Rigidly defined and Not affected by extreme values

Not based on all values, Affected by Sampling Fluctuations and is not capable of further algebraic treatment

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Unlike range, quartile deviation does not involve the extreme values. It is defined as:

Q.D=

Coefficient of Q.D=



Summary

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The measures of central tendency and measures of dispersion summarise mass data in terms of its two important features. With respect to nature of data to cluster around a central value With respect to their spread from their central value

Arithmetic mean is defined as the sum of all values divided by number of values.Median of a set of values is the middle most value when the values are arranged in the ascending order of magnitude.Mode is the value which has the highest frequency

The measures of variations are:i. Range (R)ii. Quartile Deviations ( Q.D)iii. Mean Deviations (M.D)iv. Standard Deviations (S.D)



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Check Your Learning

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State whether the following questions are ‘True’ or ‘False’.

1)Arithmetic mean is affected by extreme values.Ans: True.

2.It can be calculated for distributions with closed-end classes.Ans: False, it can be calculated for open-end classes.

3. Modal value is most useful for business people.Ans: True.

4. Quantiles are positional value.Ans: True.

5. Range is used When the study requires deep analysis.Ans: False, Range is used when study does not requires deep analysis



Activity

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1. For the distribution shown in table, find the median, mode ,quartile deviation and the coefficient of quartile deviation

% marks 0-10 10-20

20-30 30-40

40-50 50-60 60-70

No of smokers

24 22 42 16 12 18 24


Ppt Unit 04 Mbf103

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