Statistics is one of the known branches of mathematics that is used to study analytical data. The methods of statistics are generated to examine the large quantitative data and their properties.

Several companies use different statistical formulas to calculate the report of the individuals or employees. In the upcoming paragraphs, we will discuss terminologies of statistics that are used to study for different purposes.

To initiate, one needs first to recognize the definition of the statistics in terms of *sample data*** **and** ***population data***. **

The samples are one of the sub-set of the population, whereas a population is an overall set of things or individuals of a specified group.

The characteristics of the sample data are known as *statistics**,* and the characteristics of the population data are known as** ***parameters***.**

*Biostatistics *is used to study statistics for biological, a variety of research fields and topics, public health, or medical applications.

The main objective of it is to use the proper statistical techniques to get knowledge about the parameters that can affect the health of humans.

**What is statistics?**

Table of Contents

**Introduction to statistics: **Statistics is the study of the analysis, presentation, collection, interpretation, organization, and large data presentation. It can be defined as a function of the given data.

That is why statistics are combined with classifying, presenting, collecting, and arranging the numerical information in some meaningful manner.

It also facilitates interpreting several outcomes from the given data and estimating all possibilities for the upcoming applications.

With the help of statistics, one can find several measures of central data as well as the deviations of dissimilar values from the main values.

Before proceeding to the advanced terminologies of statistics, let’s check whether you understand basic terminologies of statistics, i.e., *population *and *sample.*

**Take a test of your knowledge about ***population ***and ***sample***!!!**

Select the population and sample from the given statements:

**In administrative elections, an opinion poll was taken with samples of 1,500–2,500 voters. The opinion poll is assumed to express the opinions of the voters in the whole country.**

Sample: Samples of 1,500-2,500 voters.Population: All the voters in the whole country. |

**An automobile company liked to understand whether more than 60% of the American drivers own at least a private vehicle or not. The manufacturer surveyed 15,000 private vehicle drivers over America.**

Sample: 15,000 private vehicle drivers who have been surveyed.Population: All the private vehicle drivers in America. |

**Suppose you are assigned to compute the average grade point scored in a subject at school. It would be better to select the students’ sample who visit the school. The collected data from a given samples could be the average grade point scored by the students.**

Sample: Suppose the sample of 50 students.Population: Numbers of students at the school. |

**Houston city requires to understand whether the city’s annual house income is greater than the national average or not. The city’s statisticians gather data from 2,000 households.**

Sample: 2,000 households who are being examined.Population: Numbers of households in Houston city. |

**What are the*** variable types ***that are used for ****terminologies**** of ****statistics?**

*variable types*

**Categorical (qualitative)**

**Ordinal:**It has ordered qualitative variables in the given data such as sometimes, always, never, frequently, and much more.**Nominal:**It has unordered qualitative variables in the collected data such as gender, hair color, and much more.

**Quantitative data**

**Continuous:**It has numerical variables with an infinite number of collected values, such as height and much more.**Discrete:**It consists of numeric variables that are easily counted, such as the number of bacteria and others.

**Visualizing data**

**Tables:**It has numeric conclusions of the percent values, frequencies, summary statistics, and much more.**Graphs:**It is used to represent the different numeric data in the form of:

**Scatterplot:**It is used to plot the two numeric variables.**Histogram:**It can represent the data in a bar graph view of frequencies.**Boxplot:**It can present the median, mean, range, and quartiles of the collected data. Example:

**Determine the primary terms that are refereed in the following studies**

**As per a study (conducted at a college of America), the average cumulative GPA scored by the students who graduated the previous year is 3.65, 1.50, 2.80, 3.90. Check the term**

- Sample
- Population
- Data
- Variable
- Statistics
- Parameter

**Solution:**

Sample: Number of students who have graduated last year from the college (Selection- randomly). |

Population: All students who have attended all the college classes the previous year. |

Data: 3.65, 1.50, 2.80, 3.90. |

Variable: Students’ average cumulative GPA who have graduated last year from college. |

Statistics: Single student’s cumulative GPA who graduated last year from college. |

Parameter: Students’ average cumulative GPA who have graduated last year from college. |

**You need to know the first-year student’s mean of money spent at XYZ College over the college supplies, excluding books. You randomly study 500 first-year students studying at your college. Three students spent $200, $150, and $225, sequentially. Check the term**

- Sample
- Population
- Data
- Variable
- Statistics
- Parameter

**Solution:**

Sample: 500 students of first-year who have studied at XYZ college. |

Population: Total number of first-year students at XYZ College. |

Data: $200, $150,and $225. |

Variable: The sum of money of XYZ College a first-year student used on college supplies, excluding books. |

Statistics: Average money the 500 college students used on college supplies, excluding books. |

Parameter: Average money a college student used on college supplies, excluding books. |

**A study was designed for testing the automobiles’ safety; the NTSB gathered and analyzed the data related to the effects of the automobiles crashed over the tested dummies. Below is the criterion, which they have used:**

The speed (when the cars crashed) | Location of “dummies” |

35 miles/hour | Front seat |

The dummies placed at the front seat of the car were crushed on the wall at the speed of 35miles/hour. Now, we have to understand the proportion of dummies that had head injuries. We have taken the samples of almost 75 cars.

- Sample
- Population
- Data
- Variable
- Statistics
- Parameter

**Solution:**

Sample: 75 cars selected for a random sample. |

Population: All cars have dummies in the car’s front seat. |

Data: Yes, some had a head injury, did not, or no. |

Variable: The number of dummies who would have got major head injuries. |

Statistics: The proportion of driver dummies who would have got head injuries within the samples. |

Parameter: The proportion of driver dummies in the population would have got major head injuries. |

**What ****is ****study analysis that is used as statistics basic terminology?**

Statistics analysis is basic statistical terminology used to collect, manage, analyze, summarize, manipulate, interpret, and represent quantitative data.

It can hold all aspects of collected data that involve the techniques for planning data gathering based on the structure of experiments and surveys. Statistics analysis is used to calculate the data and represent it in various trends.

Statistics analysis are based on ** three **different types:

**Bias**

There are three different types of errors that can be generated in different areas of an experiment, such as measurement technique, study design, and analyses.

The margin of error can either be under or overestimate the parameters and to false summaries. These three types of error are:

**Random (indeterminate) error:**It can evaluate the statistics data.**Systematic (determinate) error:**It can evaluate with the help of reference standards.**Gross error:**It can use to big mistakes, such as spelling each thing on the floor.

**Descriptive statistics**

Descriptive statistics are used for the measurement of the average or the standard deviation that aids in judging the data in a descriptive statistics manner.

It can be taken as the most interesting technique to obtain the different data in columns or levels of the parameters. Descriptive statistics provides an idea of the differences or similarities between the gathered data.

It can be used to characterize the collected data using tables, graphs, and numerical conclusions.

Measure of Location | ||

Mean: Average of the given information. | Median: Center point of the collected data. | Mode: The most occurring value points. |

Measure of Spread | ||

Standard deviation: Deviation of the collected information in an experiment. | Interquartile Range: The difference between the 75% and 25% of the collected data. | Range: It is the difference value of the largest and smallest values. |

**Frequency:**It is the proportion of the given data values, which is of a single variable from various variables.**Outliers:**It is known as the extreme of the data points.

**Inferential statistics**

Once the data is explored, one needs to recognize which technique should be used to judge the data that aids in detail, visualize the analysis, and make the necessary summaries about the collected data.

There are several statistical techniques that are used to deal with various kinds of experimental data and evaluate the required relationship between the given data.

It can be used to draw a summary of the population standard, which is based on the sample values:

**Confidence Intervals:**It is the combination of the standard error and sample statistics to predict the larger population parameters.**Standard Error:**It is the uncertainty of the sample average.**Statistical Tests:**These tests are used to quantify the connection between comparisons.- A statistical test can be performed depending on the number of comparisons, variable type, and the given population’s underlying distribution.
- It is used for the comparisons which are between the two or more paired or independent groups.
- The given population’s distribution can be non-parametric (no supposed distribution) or parametric (normally distributed).
- Types of statistical tests: z-test, chi-square, regression, t-test, f-test, ANOVA, correction, and much more.

**What ****is ****study design that is used as ****terminologies**** of ****statistics?**

**Study Type**

**Observational study**

Observation of the existing condition and analysis inferences.

**Case-control:**It is used to study the existing set of group dissimilarities on the result, such as w/o vs patients with the disease.**Cross-sectional:**It is the study of the experimental patients one point at a time.**Cohort:**it is used to study the instruction or step of the group of the same people who are different on certain parameters to check the effect of these factors on the result of the interest.**Experimental**

The analysts randomly assign the task to the people for treating the groups.

**Randomization:**These are the methods that are used for selecting the samples of the specific constant variables across the standardization (groups) so that the real effect can be examined.**Placebo:**It is the treatment given to a set of the group that does not have therapeutic effects.**Blinding:**It is the assignment for the treatment which is unknown for the doctor, patients, or both.**Hypothesis**

It is the detailed prediction of the scientific questions which are tested:

**Null hypothesis:**In the null hypothesis, there is no relation between the set of groups.**Alternative hypothesis:**In this, there is a relation between the set of groups.**P-value:**The probability of the tests showed the difference between the comparisons, supposing the null function as true.

**Sample sizes justifications**

The technical terminologies of statistics are used to make sure that there must be enough experiment to search a statistics difference between the set of the group when they are biologically different.

**Significance level (α):**It has the threshold where the null hypothesis can be rejected. Standard values of α consist of 0.05, 0.01, 0.001.- If the value of p is greater than α, then the test fails in the category of the rejected null hypothesis.
- If the value of p is equal to or less than α, then the null hypothesis can be rejected.
**Effect size:**It is used to check the difference between the comparison values.**Power:**It is the ability to detect the difference between the truly existed values.

**Let’s take a quick revision of all the terminologies of statistics we have discussed above!!**

Population – All objects, individuals, or measures whose characteristics have been studied. |

Variable- A feature of interest related to a specific object or person in a given population. |

Sample- It is the subset of the studied population. |

Data- A set of outcomes (a set of possible observations ); that can be separated into two groups: quantitative (a trait that is indicated by the series of a number) or qualitative (a trait that is indicated using a label). |

Parameter- A number used to describe a characteristic of the population, which is not determined easily. |

Statistic- A sample’s numerical characteristic; a statistic that measures a similar population parameter. |

Probability- A number that lies between zero & one, including a specific event that will occur. |

**Conclusion**

This blog has provided all the information about the basic terminologies of statistics that is used to study the large qualitative data.

This includes the types of variables used in statistics, different kinds of study designs, and the study analysis used as statistics terminologies.

Because of these terminologies, you can easily understand where and when to use these terminologies.

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**Frequently Asked Questions**

**What are the different definitions of statistics?**

1: Statistics is a branch of mathematics that deals with the data collection, examination, description, and display of numerical data masses.

2: Statistics is a collection of various quantitative data.

**Where are statistics used?**

Statistics is used in various aspects of life, like in robotics, data science, business, weather forecasting, sports, and much more.

**What are the basic terms of statistics?**

The big terms used in statistics are sample, population, parameter, statistic, variables, probability, and data.

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