 A variable is a factor that can assume deferent amounts. They can be controlled, dependent or independent variable. It is worth noting that variables can either be continuous or discrete variables, this is dependent on the availability of gaps that the value in question is likely to take. The value is discrete if it has such gaps but in the case that the gaps are absent then the value takes the form of a continuous variable.

Part 1

The blood pressure represented on the table is a continuous variable. It is a numeric variable. Measurements and observations can assume any values within a set of real numbers. They can be represented in fractions. The values taken by the observation can be the smallest value the instrument can allow. The blood pressure is given a provision and can take any value within the intervals. A continuous variable is such that its value must represent a set such that whenever x and y is one of the representatives of the set, it follow that every numeral between x and y is also a member of the set. Commonly used examples are the variables that are normally expressed in intervals of the number line

In case where the number of women (users and non-users) is defined then this becomes discrete data. The number of women has been identified and this has taken values basing on counts from whole variables that are distinct. They cannot assume the representation of a fraction. This is in contrast to the continuous data. It represents the numerals that can be counted to the end. It is finite and cannot take the form of fractions hence integers.

Part 2

The frequency distributions resulted to two histograms that assumed the shapes of normal curves. With class boundaries of 4, the blood pressure on the x axis and the percentages on the y axis.This study is purely observational and the women had an option to choose between users of the contraceptives or non-users. Those conducting the experiment just watched without influence. It has always been a debate relating increase in blood pressure to the users of contraceptives. The non-hormonal contraceptives are in no way liable for any blood pressure changes but in the case of the pills which are oral, it can be justified to be suspected of causing increased blood pressure. This could however be misleading as blood pressure has been proven to rise with age increase. The aging are prone to suffering from high blood pressure related cases that the young women. The control group of the non-users of these pills plays a big role in this experiment.

The two histograms for the users and the non-users depicted shapes that are similar. However; the histogram for the user is a bit higher when approaching marls 116mm and diminishing to the left. Such conclusions however need caution. The study thus indicates that the use of contraceptives by a woman results to their blood pressure going up by some few millimeters .This is however subject to judgement as research has shown that this does not happen to everybody.

Part 3

Provided a Histogram is handled with caution and corrective measures taken including the appropriate scaling, it follows the shape of the normal curve. Normal approximation is basically the transformation of the horizontal scaling of the Histogram in question so that the alignment is in line with the standard normal density curve.After normal approximation, the resulting value of data attains z units. The area under the Histogram is always the same as the area under the curve in the case that the Histogram follows the properties of the normal curve. This also follows that the area under the histogram relates with correspondence to the percentage of variable in the related interval. This normal approximation mainly aims at using the normal density curves in the approximation of percentages of variables in a certain interval.

Several data sets are approximately normal. We can always approximate the percentage of points in a set of data that lie in between two numbers. This is possible by having the numbers converted to standard units and computing the area under the standard normal curve by the use of the normal tabulation. This makes use of the normal table to estimate the ranks in percentages if the data set is approximately normal.

Descriptive statistics is used to elaborate and describe the features, characteristics and the behaviors of statistical information for the interpretation of day to day events. The experiments make the results valid and arguable as the statistics back up the facts. The results on the systolic blood pressure if taken accurately using effective mechanisms can be used to develop a histogram that is ideal. This histogram is an important tool that can be used to infer important facts when the behavior is analyzed. Although the contraceptive pills react differently to different people, the graphical representations brought out that they facilitated the rise in blood pressure to its users. The module has expounded on a lot on normal distributions and the essence of normal approximation. This has resulted to efficiency in representations of random variables in the natural and social sciences (Chen, Goldstein & Shao, 2011, p.397).