Statistics and Quantitative Methods

STATISTICS AND QUANTITATIVE METHODS

PRACTICAL CASE (Individual)

MBA 2010-2011

Story Name: TV, Physicians, and Life Expectancy.

Methods: Descriptive Statistics, Box and Whisker Plot, Correlation and Regression, Confidence Intervals and Hypothesis Testing.

Reference: http://mathforum.org/workshops/sum96/data.collections/datalibrary/data.set6.html

Description: Number of TV´s, number of Physicians and Male and Female life expectancy in 40 countries all over the world.

Number of cases: 40

Variable Names:

1.- Average Life Expectancy

2.- Male Life Expectancy

3.- Female Life Expectancy

4.- People per TV

5.- People per Physician

Television, Physicians, and Life Expectancy

Country Life expectancy People/TV People/ physician Female life expectancy Male life expectancy

Argentina 70,5 4 370 74 67

Bangladesh 53,5 315 6166 53 54

Brazil 65 4 684 68 62

Canada 76,5 1,7 449 80 73

China 70 8 643 72 68

Colombia 71 5,6 1551 74 68

Egypt 60,5 15 616 61 60

Ethiopia 51,5 503 36660 53 50

France 78 2,6 403 82 74

Germany 76 2,6 346 79 73

India 57,5 44 2471 58 57

Indonesia 61 24 7427 63 59

Iran 64,5 23 2992 65 64

Italy 78,5 3,8 233 82 75

Japan 79 1,8 609 82 76

Kenya 61 96 7615 63 59

Korea, North 70 90 370 73 67

Korea, South 70 4,9 1066 73 67

Mexico 72 6,6 600 76 68

Morocco 64,5 21 4873 66 63

Myanmar (Burma) 54,5 592 3485 56 53

Pakistan 56,5 73 2364 57 56

Peru 64,5 14 1016 67 62

Philippines 64,5 8,8 1062 67 62

Poland 73 3,9 480 77 69

Romania 72 6 559 75 69

Russia 69 3,2 259 74 64

South Africa 64 11 1340 67 61

Spain 78,5 2,6 275 82 75

Sudan 53 23 12550 54 52

Taiwan 75 3,2 965 78 72

Tanzania 52,5 * 25229 55 50

Thailand 68,5 11 4883 71 66

Turkey 70 5 1189 72 68

Ukraine 70,5 3 226 75 66

United Kingdom 76 3 611 79 73

United States 75,5 1,3 404 79 72

Venezuela 74,5 5,6 576 78 71

Vietnam 65 29 3096 67 63

Zaire 54 * 23193 56 52

Data Description

This data set contains the values of the life expectancy (for men, women and average) for 40 different countries. It also contains the number of people per TV and physician.

Without doing any statistic calculations, we can easily infer that there must be some kind of relation between the number of physicians per person and the life expectancy. We can also preview that there also has to be any relation between the number of TV´s per person and the number of physician per person because a higher number of TV´s per person will mean a higher number of physician per person too (both variables represent in any way the well-being state of a country).

However, we are going to develop some statistic methods in order to figure out what are the relations between the variables we have mentioned and see how strong are those relations.

Descriptive Statistics

We are now going to take a look at the data set graphs such as the histogram and box-and-whisker plot basically.

We will describe the average life expectancy from an statistical point of view.

First of all, we go for the scattered plot.

As we can see from the scattered plot the data are not concentrated but they are scattered along a wide range. It seems not to be any outlier and the distribution seems to have a quite significant flattered shape. We cannot say so far whether the distribution is symmetric or not but we can advance that the mean and the median should each other be very close.

So, let´s now go to the box-and-whisker plot to try to find out the rest of information.

Now we can describe more data characteristics from the chart. The first thing we see from the graph is that the distribution is not symmetric and that the mean is lower than the median. From what we have learnt, we now that when median>mean the distribution is skewed to the left. In this case we see that the distribution has a light skewed to the left. Even, from this type of distribution we can say that the mode is going to be higher than the median (we will see it when we´ll go for the histogram). We now confirm that there are not outliers (outside points, as we predicted before).

According to the box-and-whisker plot we have the following measures of central tendency:

Minimum = 51,5 Maximum = 79,0 Range = 27,5= (79,0-51,5)

First quartile= q1= percentile 25,0% = 61,0

Second quartile= q2= median= percentile 50,0% = 69,5 (which separates data in two halves)

Mean = 67,0375 (as we said before, the median and the mean are very close)

Third quartile= q3= percentile 75,0% = 73,75

Interquartile Range (IQR) = q3-q1= 73,75-61,00= 12,75

The measures of variability are the following:

Variance = 68,0434 Standard deviation = 8,24884

Finally, if we plot the histogram we will finish the descriptive analysis:

From the histogram we can confirm that the data are not symmetric. Regarding the shape of the distribution, now we see how flattered is our distribution (Stnd. kurtosis = -1,18509, negative value= platykurtic) and we see the light skewed to the left (Stnd. skewness = -1,062, negative value). These are measures of shape.

Descriptive Statistics for Male and Female Life Expectancy

One question that anyone could ask himself is whether or not men have a higher or lower life expectancy than women. In order to answer this obvious question let´s use our knowledge of statistics.

First, we are going to consider the two samples of the population, that means:

Sample 1: Female life expect: 40 values ranging from 53,0 to 82,0

Sample 2: Male life expect: 40 values ranging from 50,0 to 76,0

Without doing any calculation, we see that women have, on average, a higher life expectancy than men. We can also say that the range of variability is a bit lower for women than for men.

Women Men

Minimum 53,0 50,0

Maximum 82,0 76,0

Range 29,0 26,0

But, quite more interesting is to compare the two samples according to the box-and-whisker plots. We can get a lot of information from the analysis of these charts. Let´s see how:

Women Men

Mean 69,575 64,5 (difference of 5,075)

Variance 83,9429 55,0769

Standard deviation 9,16204 7,42138

We can confirm that, on average, women have a higher life expectancy than men.

From the box plot, we also see that the two distributions overlapped, which means that some members of each sample share common values of life expectancy.