## Introduction

Statistical methods are tools used by the psychological researcher to summarize and draw conclusions about collected and predict data about population. This research paper discusses the difference between the descriptive statistics and the inferential statistics. It has also described the measurement scales and measures of central tendency. The measures of central tendency are very useful in describing the behaviors of elements in a data set.

## Difference between descriptive and inferential statistics

According to Houser (2009), descriptive statistics are the statistical steps that are followed to describe the totality of study. He goes on to say that the data that are used on study could be gathered from either a sample of the population or a population at large. In addition, he says that the descriptive statistics gives an explanation of the data that a researcher wishes to use in his study.

Inferential statistic plays a big role in predicting the variables of a population based on the sample that the researcher used. In the inferential statistic one can get the outcome of the analysis by using the sample and can aggregate it to the whole population that the sample represents.

Descriptive statistics give the information of a group we are studying. For example, one can calculate the mean, mode and standard deviation of the scored which 50 students get in an exam. Through the analysis of the data, the researcher is able to explain the behavior of the elements of a data set and the population as a whole. The population should be large enough and must explain the traits that the researcher is seeking to find. In the inferential statistics, the researchers use the sample to represent the whole population. They ensure that the sample accurately represents the population (Brian, 2001).

The objective of the inferential population is to identify the characteristic or the general pattern of a large population by analyzing a sample of the population. The result of the sample is taken to represent the whole population.

## Measurement scales

According to Larry (2009), interval scale can be defined as measures that ensure that the intervals used in ranking by the researcher are equal. The scale that the researcher uses can either be added or subtracted. For example, equal differences on the temperature scale indicate equal differences in the temperature. If there is difference of 2°F in the temperature scale, it indicates the difference of 2°F in the temperature.

The difference between the ratio scale and the interval scale is that the ratio scales have zero points and it is major or main measurement scale. The researcher can be able to use the ratio scale to calculate valuable ratios. For example, a temperature of 100°K is twice as high as a temperature of 150°K

Ordinary scale allows the researcher to arrange the data which has more and which has less quality but they do not allow the researcher to say how much more or less.

## Measures of central tendency

Central tendency refers to some value in a data set that is used as a representative of the whole data. The most common measures are the mode, mean, and median. According to Houser (2009), when all the data representing the population are organized in an ascending order or descending order, the value in the middle position is called the median. He says that the median cut the frequency distribution in two equal parts and therefore, it can be said to be 50^{th} percentile.

If the population in the study is odd, the median can be calculated using the formula (*n* + 1)/2th population, but where the number of the population is even the value of the median is determined using *n*/2th and (*n*/2 + 1) of the population. Median is easy to calculate and to understand as compared with other measure of the central tendency, but it does not use all the information in the data (Kenneth, 2007).

Mode is a measure of central tendency and it only takes care of one value in a data set. According to Houser (2009), the mode can be defined as the most frequently occurring value in a given data. He continues to say that some sets of data do not have mode as the values in the data do not occur twice or they only occur one time. In addition, a given set of data can have two or more modes where a given data has two or more values of equal frequency. Mode is easily calculated as compared with mean and mode.

The central tendency can also be measured using mean. Mean is the value representing all the elements in a data set on average. It is obtained by dividing the value of entire data by the number of elements under study.

## Conclusion

Statistics assist the researcher in collecting, analyzing and interpreting the numerical data. Statistics involves two processes that are describing sets of data and drawing conclusions. The data may be described using descriptive statistics such as measures of location, dispersions and location.

## Referencing List

Brian, E. (2001). *Statistic* *for Psychologists: An Intermediate Course*. New York: John Wiley & Sons, Inc.

Houser, R. (2009). *Counseling and Educational Research: Evaluation and Application **(2nd Ed.)*. Thousand Oaks, CA: Sage.

Kenneth, N (2007). *Modern Mathematical* *Statistics* *with Applications*. Baltimore: Johns Hopkins University Press.

Larry, B. (2009). *Statistics* *for the Behavioral Sciences*. Kansas: Federal Reserve Bank of Kansas City.