Descriptive Statistics

Descriptive statistics involves the interpretation of data in a simplified form; it involves summarizing the basic futures of data. Descriptive statistics involves calculation of the population or *sample* mean, median, mode and dispersion; dispersion measures include the variance and standard variations. It also involves the description of distribution of data through establishing the frequency of classes or scale established.

We take the US population release in 2000 retrieved from http://www.census.gov/population/w ww/cen2000/briefs/phc-t1/index.html

, the data contains several races to describe the contents of the data, and the following is a summary of the data:

RACE

over 18 years

below 18 years

total

percentage

Descriptive Statistics

Total population

209 128 094

72 293 812

281 421 906

White

161 862 337

49 598 289

211 460 626

75.14%

Black or African American

Descriptive Statistics

23 772 494

10 885 696

34 658 190

12.32%

American Indian and Alaska Native

1 635 644

840 312

2 475 956

0.88%

Asian

7 777 999

Descriptive Statistics

2 464 999

10 242 998

3.64%

Native Hawaiian and Other Pacific Islander

271 656

127 179

398 835

0.14%

Some other race

9 838 622

5 520 451

Descriptive Statistics

15 359 073

5.46%

Two or more races

3 969 342

2 856 886

6 826 228

2.43%

The distribution of the data will be summarized in a graph as follows:

The above chart summarises the US 2000 population with reference to race, it is evident that whites are the majority and native hawaian have the lowest number of people. We can establish the mean, medsian and the mdoe for the selected data and from the calculations the mean is 40 203 129 while the standard deviation is 76372390.43. This means that the average value for the

Descriptive Statistics

data is 40,203,129, the standard deviation value means that the data deviates 76372390 from the mean, this is a large value of standard deviation meaning that the data deviates more; this means that we have very low and very high values in the data. The mode is the value that has the highest frequency, in our case we don’t have the *mode* in our data, the median value for our data is 10 242 998 and this is the population of Asian

Descriptive statistics and its relationship to my profession:

Descriptive statistics is important in that it provides an overview of the data in question, example from the above data we can easily establish the probability of choosing an Asian randomly from the population, it also helps to determine the number of expected consumers, example each race will have their own unique demand for products and as a person who wants to start a business in the united states then there is need to know the population size and population characteristics in terms of demand.

In business therefore descriptive statistics helps in making conclusions about various issues and therefore helps in making decision. Description statistics is the **first** step in analyzing data before making inferences of data, therefore it is important in analyzing any data collected that will help in describing the characteristics of data collected.

Probabilities:

Some of the types of probability I have encountered in my profession include joint probability and conditional probability, conditional probability is the probability of an event X happening if event Y happens, it is important in many fields of business in that it helps to make decisions under uncertainties. The other is joint probability and this is the probability where event Y happens and event X happen. Both probabilities are useful in decision making and even forecasting, for example one may observe historical data of his or favorite team wins and losses during cold and warm climates, this will help to give an estimate in future on the probability that the climate is cold and the team wins or the probability that the climate is warm and the team

Descriptive Statistics

wins.

Use of probability:

Business decision may be based on probability, many games that exist also depend on probability example the card game, when the decision is faced with decision on investment the business may want to know the probability of achieving certain levels of profits and also the probability of being awarded these contracts, in this case therefore the firm will collect all relevant data and analyze the best option that will yield high profits and yet yield a high probability of occurrence.

Probability is also used in personal decision making, example during cold weather an individual will make the **decision** of wearing warm cloths because there is a high probability that it will rain, however during warm seasons decisions will wear light cloths because there is a high possibility that there will be no rain.

**Misleading** probabilities:

The use of probabilities in decision making requires that all the factors that may affect chances are taken into consideration, further if probabilities are based on historical occurrences then there is a risk of making wrong decision because what happened in the past may not happen in future.

Descriptive Statistics

Probability ranges from 0 to 1 and a probability level 0 means that we a certain that the event will not occur, the value 1 means that we are certain that the event will occur, in most cases however the probability level may be less than one and greater than 0 meaning that we are not certain that the anticipated event may not occur, therefore decisions made are based on chance and we are not certain that they will occur.

Probability only gives a measure of the level that an event will occur and the event will not occur, __decisions__ based on the probability level which is not equal to one then we are not certain that they will occur and therefore there is a risk of failure which will depend on the probability level.

Finally probability may lead to wrong decision where we may base our values on unreliable and outdated data, there is need to use reliable and up to date data that will help reduce errors in the calculation of these probabilities.

References:

Bluman A. (*2000*) Elementary Statistics: A Step by Step Approach, McGraw Hill press, New York

US Census (**2008**) 2000 **Census** data, retrieved on 17th July, available at http://www.census.go v/population/www/cen2000/briefs/phc-t1/index.html

Descriptive Statistics

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