Independent and dependent variables are arithmetical tools used in a research to keep trail of what’s going on. They permit you to uphold control over your research in a quantitative way. (Schwab, 2004, p. 65)

The independent variable is a variable in an equation that may possibly have its value liberally chosen without taking into account values of any additional variable. A good illustration can be seen in an equation such as y = 8x – 4, the independent variable is x. In an nutshell, an independent variable is a variable which can be assigned any allowable value with no any limit imposed by any additional variable. (Austin & Pinkleton, 2001, p. 79)

A dependent variable on the other hand is a variable that depends on one or more other variables. If we go back to our equation; y = 8x – 4, the dependent variable is y. The value of y depends on the value selected for x. It should be noted that a dependent variable is more often than not isolated on one side of an equation. In an nutshell, a dependent variable is a variable in an equation, function or expression that has its value dogged by the option of value(s) of other variable(s). (Schwab, 2004, p. 72)

In calculus, the identification of the self-governing and reliant variable is important, in the sense that the rate of change, or copied, of the reliant variable is designed with respect to the self-governing variable. Dependent and independent variables refer to values that alter in affiliation to each other. The reliant variables are those that are observed to alter in reply to the independent variables. The independent variables on the other hand, are those that are intentionally manipulated to appeal to a change in the reliant variables. For instance, “if x is given then y occurs”, where x stands for the independent variables and y stands for the dependent variables. (Austin & Pinkleton, 2001, p. 90)

While independent variables are also identified as forecaster variables, controlled variables, descriptive variables, regressors, manipulate variables or input variables; reliant variables on the other are also identified as the regress variable, the experimental variable, the responding variable, the result variable, the output variable, just to mention but a few. (Schwab, 2004, p. 83)

In an experimental research, the investigator manipulates at least one variable and subsequently measures at least one result. Manipulated variables are termed as self-governing variables while outcome variables are termed as dependent variables. A self-governing variable is a variable whose value determines the value of additional variables. The dependent variable depends on the result of the self-governing variables. Name and define the measures of central tendency and of variability

Central tendency is an arithmetical measure that identifies a particular score as envoy of a whole distribution of scores. The objective is to discover the single score that is the most envoy of the whole distribution. Unluckily, there is no single, normal procedure for determining central tendency. There are three main measures of central tendency mainly; the arithmetical mean, the median and the mode. (Lodico et al, 2006, p. 103)

Atithmetic mean has merits and demerits. These include the following: (Lodico et al, 2006, p. 105)

Merit:

- Quick and simpe to compute.
- Used for deduction and description; best estimator of the parameter.
- It’s based on all information in the distribution.
- Most frequently used statistic for central tendency.

Demerit:

- It may not be an envoy of the entire sample.

Median this is the middle value of all the figures in the sample after they have been put into an ascending order. In additional words, the median is the value that divides the set of figures in half, 50% of the remarks being above or equal to it and 50% being below or equal to it. (Lodico et al, 2006, p. 107)

In the case of an odd number of remarks, there is only one middle number. In the case of an even number of remarks, there are two middle numbers and the median is the mean of them. It should be noted that the median divides the observations into equal parts. (Schwab, 2004, p. 96)

Median can be computed as (n+1)/2, where, n is the number in a list, after they have been put in an ascending order. (Schwab, 2004, p. 101)

It has various merit and demerits such as; (Schwab, 2004, p. 104)

Merit:

- It takes all figures into account equally.

Demerits:

- Its more tedious to compute than the other two.
- It can be affected by a few extremely bulky or extremely small numbers.

Mode this is the most commonly experiential value of the measurements in the sample. There can be more than one mode or no mode at all in central tendency. For instance; for an even numerical of values, the median is the average of the middle two values. For an odd numercal of values, the median is the middle of all the values. (Lodico et al, 2006, p. 110)

Some of the merits and demerits include; (Lodico et al, 2006, p. 113)

Merit:

- Its quite easy to compute, and half of the sample usually lies above the median.
- Good for nominal variables.
- Good if you need to know most frequent observation.

Demerit:

- It’s tiresome to compute a large sample which is not in order.

Variability offers a quantitative gauge of the degree in which scores in a distribution are spread out. The superior the dissimilarity between score, the more spread out the distribution is. The more compactly the scores are grouped together, the less variability there is in the distribution. The most regularly used methods of dimension of this variance are; range, interquartile range, deviation and variance, and standard deviation. (Lodico et al, 2006, p. 116)

The range of a distribution is defined as the dissimilarity between the largest and smallest values of a changeable in the sample. For example, in the distribution [1 5 4 10 7 3], the range would be 10-1 = 9. From this illustration, the range only takes into consideration two numbers mostly, the highest and the lowest. This demonstrates that it’s a somewhat a crude measure of variability. (Lodico et al, 2006, p. 118)

The interquartile range (IQR) is a range that contains the middle 50% of the scores in a distribution. It is calculated as follows: IQR = 75th percentile – 25th percentile. (Lodico et al, 2006, p. 119)

Semi-interquartile range is a correlated measure of variability. It is calculated as interquartile range divided by 2. (Lodico et al, 2006, p. 120)

Variance can be defined as a gauge of how close the scores in the distribution are to the center of the distribution. For example, using the mean as the measure of the center of the distribution, the variance is described as the average squares dissimilarity of the scores from the mean. It should be noted that, when the scores are heterogeneous, the measure of variability ought to be great and vice versa. (Lodico et al, 2006, p. 121)

The standard deviation is a particularly helpful measure of variability when the distribution is standard or roughly normal since the proportion of the distribution within a given number of standard deviations from the mean can be premeditated. For that reason, standard deviation is the average distance from the mean. Consequently mean is the envoy value, and the standard deviation on the other hand is the envoy distance of whichever one point in the distribution from the mean. (Lodico et al, 2006, p. 130)

Despite the fact that the measures of central tendency convey information concerning the commonalties of calculated properties, the measures of variability on the other hand, measure the degree to which they vary. If currently all values of data are identical, they vary and variability exists. Therefore, the measures of central tendency ought to be harmonized by measures of variability for similar reason.

Recognizing and writing survey questions are significant facets of any survey procedure. It should be noted that survey items are the construction blocks of the survey. The way in which the survey questions execute, the sufficiency with which they acquire the desired information, has a superior influence on the outcome of the survey than any other single part of the procedure. These survey questions include; open ended, multiple choice and likert scales. (Austin & Pinkleton, 2001, p. 101)

Open ended questions seek to discover the qualitative, in detail aspects of a particular theme. It permits the respondent to answer in detail; however, it places few constraints on the nature of their reply. They are also termed as free response or free answer questions; this is because the partakers are free to answer the question in any way they choose. (Austin & Pinkleton, 2001, p. 104)

Multiple choice questions limit’s the respondent’s reply to the survey. The partakers are permitted to choose from whichever a pre-existing set of dichotomous answers, such as true/ false, yes/no, or multiple choices with an alternative for “other” to be filled in, or ranking scale reply options. (Lodico et al, 2006, p. 96)

The likert scale is one of the most extensively used itemized scales. The ending points of a likert scale are characteristically strongly disagree and strongly agree. Here, the respondents are asked to point out their degree of agreements by checking one of five response grouping mainly; strongly disagree, disagree, neither agree nor disagree, agree, and strongly agree. (Austin & Pinkleton, 2001, p. 105)

Multiple choice questions decrease changes of interviewer’s favoritism opinion on a particular topic. In addition to this, their questions are well managed and structured towards the objective of the survey compared to open ended survey questions. (Lodico et al, 2006, p. 99)

Whereus open ended questions are helpful in exploratory research as opening questions, multiple choice questions or likert scales on the othe hand are beneficial in large surveys. (Austin & Pinkleton, 2001, p. 106)

Open ended, multiple choice and likert scales have their own pros and cons.

Advantages of open ended:

- Research indicates that they are superior for bringing out sensitive information, such as information regarding sexual assault or drug usage. (Austin & Pinkleton, 2001, p. 115)
- They cut down to two kinds of reply error mainly, respondents are not probable to forget the answers they have to pick from if they are given the possibility to act in response freely; and that they do not permit respondents to ignore reading the questions and just “fill in” the survey with all similar answers. (Austin & Pinkleton, 2001, p. 118)
- They permit respondents to take in more information, counting feelings, attitudes and understanding of the theme. This permits researchers to better access the respondents’ true feelings on a subject. (Lodico et al, 2006, p. 60)

Disadvantages:

- They can lead to recurrence, gathering of immaterial information,and misinterpretation regarding the intention of the question since they hearten the respondents to respond in their own terms. (Austin & Pinkleton, 2001, p. 120)
- Results obtained are more often than not more complicated to analyze. (Lodico et al, 2006, p. 61)
- Since the questions are examined quantitatively, it then follows that the quantitative information is reduced to coding and answers have a tendency of losing some of their initial meaning. (Austin & Pinkleton, 2001, p. 123)

Advantages of multiple choice:

- They are more easily analyzed in the sense that each and every answer can be given a number so that an arithmetical interpretation can be assessed. (Lodico et al, 2006, p. 62)
- They are better suitable for computer analysis. (Lodico et al, 2006, p. 65)
- They can be more precise, thus more probable to converse alike meanings. (Austin & Pinkleton, 2001, p. 126)
- They take less time from the interviewer, the partaker and the researcher and thus a less expensive survey method. (Austin & Pinkleton, 2001, p. 130)

Disadvantages:

- Because of their simplicity and limit of the answers, they may not offer the respondents choices that in fact reflect their real feelings. (Austin & Pinkleton, 2001, p. 133)
- They do not permit the respondents to give details that they do not comprehend the question or do not have an opinion on the issue. (Austin & Pinkleton, 2001, p.135)
- It is difficult to build up effective multiple choice questionnaires. (Austin & Pinkleton, p. 136)

Advantages of Likert Scale:

- It is easy for the investigator to build and manage. (Lodico et al, 2006, p. 67)
- It is easy for the respondent to comprehend. (Austin & Pinkleton, 2001, p. 140)
- It is appropriate for mail, cellular phone, individual or electronic surveys. (Austin & Pinkleton, 2001, p. 140)
- It is extensively used in advertising surveys. (Austin & Pinkleton, 2001, p. 140)

Disadvantages:

- It takes longer to complete than other list ranking scales. (Austin & Pinkleton, 2001, p. 141)

Many investigators use a mixture of multipled and open ended questions, preferably multiple choice questions in the commencement of their survey, and then permit for more liberal answers once the respondent are recognizable or have some backdrop on the issues represented.