The branch of mathematics dealing with numerical data. (See mean, median, mode, normal distribution curve, sample, standard deviation, and statistical significance.)
Statistics, the science of collecting, analyzing, presenting, and interpreting data. Governmental needs for census data as well as information about a variety of economic activities provided much of the early impetus for the field of statistics. Currently the need to turn the large amounts of data available in many applied fields into useful information has stimulated both theoretical and practical developments in statistics.
Descriptive and inferential statistics are two broad categories in the field of statistics. In this blog post, I show you how both types of statistics are important for different purposes. Interestingly, some of the statistical measures are similar, but the goals and methodologies are very different.
Descriptive Statistics
Inferential Statistics
Inferential statistics takes data from a sample and makes inferences about the larger population from which the sample was drawn. Because the goal of inferential statistics is to draw conclusions from a sample and generalize them to a population, we need to have confidence that our sample accurately reflects the population. This requirement affects our process. At a broad level, we must do the following:
- Define the population we are studying.
- Draw a representative sample from that population.
- Use analyses that incorporate the sampling error.
A population is the entire group that you want to draw conclusions about.
A sample is the specific group that you will collect data from. The size of the sample is always less than the total size of the population.
In research, a population doesn’t always refer to people. It can mean a group containing elements of anything you want to study, such as objects, events, organizations, countries, species, organisms, etc.
What is Parameter?
A parameter is a useful component of statistical analysis. It refers to the characteristics that are used to define a given population. It is used to describe a specific characteristic of the entire population. When making an inference about the population, the parameter is unknown because it would be impossible to collect information from every member of the population. Rather, we use a statistic of a sample picked from the population to derive a conclusion about the parameter.
Most Common Parameters
The most commonly used parameters are the measures of central tendency. These measures include mean, median, and mode, and they are used to describe how data behaves in a distribution. They are discussed below:
1. Mean
The mean is also referred to as the average, and it is the most commonly used among the three measures of central tendency. Researchers use the parameter to describe the data distribution of ratios and intervals.
The mean is obtained by summing and dividing the values by the number of scores. For example, in five households that comprise 5, 2, 1, 3, and 2 children, the mean can be calculated as follows:
= (5+2+1+3+2)/5
= 13/5
= 2.6
2. Median
The median is used to calculate variables that are measured with ordinal, interval, or ratio scales. It is obtained by arranging the data from the lowest to the highest and then picking the number(s) in the middle. If the total number of data points is an odd number, the median is usually the middle number. If the numbers are even, the median is obtained by summing the two numbers in the middle and dividing them by two to get the mean.
Median is mostly used when there are a few data points that are different. For example, when calculating the median of students entering college, there may be a section of students who are older than the rest. Using the mean may distort the values since it will show that the average age of students entering college to be higher, whereas using the median can give a truer reflection of the situation.
For example, let’s find the median age of students entering college for the first time, given the following values of ten students:
17, 17, 18, 19, 19, 20, 21, 25, 28, 32
The median of the values above is (19+20)/2 = 19.5.
Mode
The mode is the most occurring number within a data distribution. It shows what number or value is the highest in number or most common in the data distribution. The mode is used for any type of data.
For example, let’s take the example of a college class with about 40 students. The students are given a test exam, graded, and then grouped on a scale of 1-5, starting with students with the lowest number of marks.
The marks are graded as follows:
- Cluster 1: 5
- Cluster 2: 7
- Cluster 3: 13
- Cluster 4: 12
- Cluster 5: 3
Cluster 3 shows the highest number of students and, therefore, the mode is 13. It reveals that out of 40 students, most of the students were graded in cluster 3.
Data
We do not generally associate data with mathematics. However, data is the base of all operations in statistics. So let us learn more about data collection, primary data, secondary data, and a few other important terms.
What is Data?
Data can be defined as a systematic record of a particular quantity. It is the different values of that quantity represented together in a set. It is a collection of facts and figures to be used for a specific purpose such as a survey or analysis. When arranged in an organized form, can be called information. The source of data ( primary data, secondary data) is also an important factor.
Types of Data
Data may be qualitative or quantitative. Once you know the difference between them, you can know how to use them.
- Qualitative Data: They represent some characteristics or attributes. They depict descriptions that may be observed but cannot be computed or calculated. For example, data on attributes such as intelligence, honesty, wisdom, cleanliness, and creativity collected using the students of your class a sample would be classified as qualitative. They are more exploratory than conclusive in nature.
- Quantitative Data: These can be measured and not simply observed. They can be numerically represented and calculations can be performed on them. For example, data on the number of students playing different sports from your class gives an estimate of how many of the total students play which sport. This information is numerical and can be classified as quantitative.
