# Descriptive Statistics

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The numbers that are used in the summarizing and describing of data constitute what is called descriptive statistics. Data can be any information collected from a survey, experiment or a historical record. For instance if one is analyzing the birth certificates of children from a given State, then the percentage of certificates given out in that state or the average age of mothers, can constitute the descriptive statistic of the data. Any number that is used in the computation is also taken as a descriptive statistics for the data from the computed statistic. A number of descriptive statistics may be used at once for better description of the data (Lane, 2003).

There are various ways in which statistical data can be interpreted. This includes measures of central tendency and measures of dispersion. This provides shorthand in the description of the distribution of data. Measures of central tendency include the mean, mode and median. Measures of dispersion are the range, variance and standard deviation (Ryan, 2004).

For example in a survey carried out to examine the dominance of risk factors for cardiovascular disease, a measurement of systolic blood pressure was done twice on each patient to ascertain the reliability of the measures. A calculation of the difference between the measures was done for each of the 10,000 patients and relative distribution of the same plotted. The mean difference was found to be 0 mmHg and standard deviation was 2 mmHg. Since the distribution was symmetrical, it was estimated that 95% of the difference lay within 4 mmHg of the mean, 0. So from this, if a person’s measures differ by 4 mmHg then this will be unusual and therefore has a risk of getting a cardiovascular disease. This will call for the necessary measures to be taken in terms of treatment. Or in the estimation of birth weight that is symmetrically distributed in a population. The proportion of babies who will weigh less than 2000 grams can be calculated. If the newborns’ mean weight is 3500 grams and standard deviation is 750 grams, then if there is no other information, 0.025 or 2.5% of the newborns will weigh less than 2000 grams because this is two standard deviations below the mean (Arsham, 2010).

Still in the medical world data collection and interpretation should be done very carefully as it is likely to affect the livelihood of others. This is especially in the case of public health whereby governments need to take measures in advance concerning various issues basing their judgment on the interpretation of the current statistics. There are different types of probabilities that can be used, these are; marginal probability, conditional probability, joint probability and union probability. These can be used in different methods such as the classical method of probability, the relative frequency of occurrence and the subjective probability. The most misused probability is the subjective probabilities. They are based on an individual’s intuition, feelings or experience. In this world almost every person has an opinion and would like to share it. They are not unethical to use but can be misleading and disastrous to decision makers. This is especially in the medical field where all the actions need to be justified. Operating on intuitions ca n be very risky and might lead to loss of lives. What a person needs to know is that the rules and laws of probability are for the long run (Arjomand, 1996)

For example if a coin is tossed, even though we know that the probability of getting a head is 5, the result will not obviously be a head and one can not get a half head. But on several tosses a head will be got. Take for instance an oil prospecting company , suppose the probability that it will strike oil is 10, this means that in the long run, if enough holes are drilled, the company should strike oil in about 10% of the holes. What if the company has just enough money to drill one hole? This means that it will either get a dry hole or strike oil. If this is not put into consideration, the company’s decision to drill oil might be disastrous. Classical statistics on the other hand could be used unethically to lure companies or clients into making short-run investments hoping to get something in return when in actual terms the company or client may win or lose. In the case of the oil company, it will not get back 10% by drilling one hole; it will either win or lose (Black, 2009)

Conclusion

In descriptive statistics there is always a tendency for people to ignore examining data thoroughly by descriptive means. They tend to rush on applying statistical tests on the given data without confirming whether the data is accurate. People involved in dealing with descriptive statistics should therefore always strive to take time to examine descriptively a set of data using different perspectives to get a clear picture of it. This way they will be able to discriminate against much sense and nonsense. The types of probability that exist are the marginal probability, the conditional probability, the joint probability and the union probability. The classical method of assigning probability relies on events prior or before they take place. The relative frequency of occurrence assigns probability basing on empirically derived data or historical data. Subjective probabilities on the other hand rely on the knowledge, feelings and personal experiences in assigning probability (Statistics, 2006).

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