## The use of stratified random sampling

Stratified random sampling is a method of sampling where the entire population has a particular number of elements. The entire population is divided into small manageable units. These divisions are referred to as strata. The division may be done according to age, gender, religion, or any other relevant criteria. The strata act as a source of information for the research and to ease data collection, sampling is done in each stratum. A known number of observations are then obtained from each sample. This technique may be used when the accuracy and precision of the data obtained from the research are of paramount importance. The stratified sampling method is more accurate and precise as opposed to the simple sampling technique of the same size.

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The division of the population into strata ensures that information is obtained from all the different categories that comprise the population. The technique may also be employed when the data is diverse or heterogeneous. This is a situation where the data within a stratum is closely related but differ considerably when different strata are compared. The application of this technique in this case ensures that the strata that share the same data in the population are grouped together while those whose data is different are put in other groups. This ensures that the analysis is done easily and in a more guided way.

A stratified random sampling technique also comes in handy when the study is concerned with issues that are considered a minority within the population. These issues become easily accessible when the population is divided into strata. Another situation where stratified random sampling can be employed is where the population is large. The division of the population into strata ensures that the accessibility to different parts of the population is made possible. The research can also be divided. This ensures that different strata are attended to by the different individuals. This ensures that the time taken to complete the research is reduced considerably.

## The meaning of a process being in statistical control

When a process is in statistical control, the methods used in its analysis are statistical. The procedures of statistical process control are used to monitor this process and ensure that correct results are obtained. In case of any deviation from the expected values, corrective measures are taken to ensure that the results are brought back to the required values. The tools that are used in statistical process control include control charts. These charts are used to record data. Through the analysis of this data, any unusual event that may occur can easily be identified. This is mainly by carrying out comparisons between the obtained results and those expected and checking if there are any deviations.

Tests are also carried out to ensure that the processes that may be out of control are determined. Corrective measures are then made to ensure that the process is brought back under statistical control. The monitoring ensures optimal results are obtained from all the processes that are controlled by the statistical process control. The optimization of these processes ensures that wastes that may have developed during the process are minimized. A process under statistical control also results in reduced process time. This is advantageous in a production setup as it results in an increase in the output of the production process.

## Variables

A variable refers to a measurable quantity whose values change depending on the conditions to which it is subjected to. Variables can be broadly categorized into quantitative and qualitative. A quantitative variable always adheres to some scale. The scale acts as a guide from where comparisons between measurements are made. For example, if the length of a string is measured to the nearest metre, then one metre in this case is the fixed unit of measurement for measuring the string lengths. A qualitative variable on the other hand is a variable that may be used to indicate the category within which a unit in the population belongs. The types of variables that are within this broad categorization of variables include ratio, interval, nominal and ordinal variables.

### Ratio variables

These are quantitative variables. The ratios of values of the measurements of ratio variables are considered meaningful. The value of zero for these variables is defined. Examples of these types of variables include age, distance, time, height, and weight. For example, if the length of a string is zero then the string does not exist since this value acts as the starting point and cannot be quantified. On the other hand, if the length of a string is said 30cm, then this string’s length is three times the string whose length is 10cm. This shows the quantitative nature and also the inherent defined zero value.

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### Interval variables

These are quantitative variables. These variables have values whose ratios are not meaningful. The value of zero in these variables is not defined. The number of interval variables is limited since many variables do not possess these properties. An example of an interval variable is the temperature in Fahrenheit scale. This is an interval variable since when the temperature reads zero, there is still some warm presence.

The zero reading does not signify the absence of heat but it just shows that the amount of heat that is present is small. The ratios of temperature are not meaningful since you cannot conclude that when the temperature is 10^{o}F, the heat is twice that which will be present when the temperature reads 5^{o}F. Most variables are therefore ratio variables since their ratios are meaningful.

### Ordinal variables

These are qualitative variables. They contain categories that are ranked. Therefore, ordinal variables have a meaningful kind of ordering. An ordinal variable may either be numerical or non numerical. These types of variables are mostly used when a scale is used to rate activities or events. The use of a scale means that the different parameters that are present on the scale hold meaningful weights that are distinguishable.

For example, one may be required to rate the delivery of service of the government public service. The options that may be available to choose the ratings from may include excellent, good, fair, and bad. In this case, excellent is considered to be at a higher positive level than good which is at a higher positive level than fair. Fair is also at a higher positive level than bad. These options are sometimes replaced by numbers. In this case, the scale is represented by numerical values.

### Nominal variables

These are qualitative variables. These variables are different from ordinal variables as their categories are not ranked. Therefore, it does not have a meaningful ordering of its categories. An example of a nominal variable may be the gender of a person or the person’s place of residence.