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4. Shape of a Distribution

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Statistics for International Business

Universidad de Londres

3.6 (126 calificaciones) | 3.8K estudiantes inscritos

Curso 4 de 6 en International Business Essentials Programa Especializado

This course introduces core areas of statistics that will be useful in business and for several MBA modules. It covers a variety of ways to present data, probability, and statistical estimation. You can test your understanding as you progress, while more advanced content is available if you want to push yourself. This course forms part of a specialisation from the University of London designed to help you develop and build the essential business, academic, and cultural skills necessary to succeed in international business, or in further study. If completed successfully, your certificate from this specialisation can also be used as part of the application process for the University of London Global MBA programme, particularly for early career applicants. If you would like more information about the Global MBA, please visit https://mba.london.ac.uk/. This course is endorsed by CMI

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De la lección

Using Measures to Describe Data

This week we will describe and summarize the information in the data using numerical values or measures that are able to summarise information. This is a crucial extension to the analysis of the previous week. While graphs are informative it is usually crucial for improved understanding of the data at hand to discuss their numerical properties. In this week, we will look at a range of measures, such as measures of central tendency, the range, variance, standard deviation, and so on.

Introduction- Using Measures to Describe Data2:58

1. Descriptive Statistics- Using Measures to Describe Data3:19

2. Measures of Central Tendency and Location8:27

3. Mean, Median, and Mode- Which is Best?3:02

4. Shape of a Distribution5:43

5. Measures of Variability12:52

5.1 Measures of Variability: Examples9:50

6. Weighted Mean1:35

7. Measures of Relationships Between Variables4:27

Impartido por:

George Kapetanios
Professor of Finance and Econometrics

[MUSIC]

In lecture one, we described graphically,

the shape of a distribution as symmetric or skewed by examining a histogram.

If the center of the distribution is located at the median of the distribution

and then divides the graph of the distribution into two mirror images,

then the distribution is said to be symmetric.

Apart from a visual point of view that is by using graphs,

we can also describe the shape of a distribution

numerically by computing a measure of skewness.

The skewness is positive if the distribution is skewed to the right.

The skewness is negative for distributions skewed to the left.

Finally, the skewness is equal to zero for

distribution, such as the bell shaped distribution,

which are symmetric around the mean.

If we look at this skewed left distribution,

we can spot that the mean is less than the median.

If the distribution is skewed right, the mean is usually greater than the median.

In a symmetric distribution, the mean and the median are equal.

Notice that this relationship between the mean and

the median is usually true for continuous numerical variables.

It may not be true for discrete numerical variables or for

some continuous numerical variables.

An example of a typically skewed distribution refers to the incomes.

In fact, the distribution of incomes is often right skewed.

This is due to relativity small portion of ith values,

which compose the distribution.

The median is the preferred measure to describe the distribution

of incomes in a city, or in a state, or country.

On the one hand, we have that large portion of

the population has relatively modest incomes.

On the other hand, a small proportion of the population have a very high income.

In these cases the value of the mean is inflated by

the very wealthy portion of the population.

However, this is a too optimistic picture of the economic conditions.

In this case,

the mean of such distributions is well higher than the median.

This is why in this case, the median is the perfect measure.

This does not mean that we always have to prefer the median

to the mean when a population or a sample is skewed.

Our reasoning gives us just the insight as to why

the choice of the numerical measure is context specific based.

There are examples for which the mean should

be the preferred measure even if the distribution is skewed.

The distributions of claim sizes in an insurance company,

it is likely to be right skewed.

Now, if the company is interested in knowing

the most typical claim size we should perfect the medium as a measure.

But if the company is more interested in knowing how much money

is needed to cover the claims, then the mean should be preferred.

Notice that in spite of the advantage of the median in discounting

extreme observations, still, the mean tends to be the preferred measure.

As we will see in lecture three the mean has certain

properties which make it more attractive than the median.

The main reason is that the theoretical development of differential procedures,

based on the mean and the measures related to it is small

step forward than the procedures based on the median.

This makes the mean more efficient than the median.

[MUSIC]

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