Describing Data Discover Story (2024)

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Describing data effectively involves summarizing its key characteristics and highlighting interesting patterns or trends. Therefore, to extract information from the sample one needs to organize and summarize the collected data. The arrangement (organization) of data into a reduced form which is easy to understand, analyze, and interpret is known as the presentation of data.

Remember: our goal is to construct tables, charts, and graphs that will help to quickly reveal the concentration and shape of the data. Graphical Presentation of Data help in making wise decisions.

Visualizations: Describing Data Visually/ Graphically

Charts and graphs are powerful tools for showcasing data patterns and trends. In this article, we will discuss bar graphs and histograms only.

Describing Data Using Bar Graph

Bar diagrams can be used to get an impression of the distribution of a discrete or categorical data set. They can also be used to compare groups, and categories in explanatory data analysis (EDA) to illustrate the major features of the data distribution in a convenient form.

A graphical representation in which the discrete classes are reported on the horizontal axis and the class frequencies on the vertical axis and the class frequencies are proportional to the heights of the bars. It is a way of summarizing a set of categorical data.

Note that a distinguishing characteristic of a bar chart is that there is a distance or a gap between the bars i.e. the variable of interest is qualitative and the bars are not adjacent to each other. Thus a bar chart graphically describes a frequency table using a series of uniformly wide rectangles, where the height of each rectangle is the class frequency.

There are different versions of bar graphs such as clustered bar graphs, stacked bar graphs, horizontal bar graphs, and vertical bar graphs.

Describing Data: Bar Graphs

Describing Data in Histogram

A histogram is a similar graphical representation to bar graphs. It is used to summarize data that are quantitative i.e. measured on an interval or ratio scale (continuous). Histograms are constructed from the grouped data by taking class boundaries along the x-axis and the corresponding frequencies along the y-axis. The heights of the bars represent the class frequencies.

Note that the horizontal axis represents all possible values because the nature of data is quantitative which is usually measured using continuous scales, not discrete. That is why, histogram bars are drawn adjacent to each other to show the continuous nature of data. It is generally used for large data sets (having more than 100 observations) when stem and leaf plots become tedious to construct. A histogram can also help in detecting any unusual observations (outliers) or gaps in the data set.

Describing Data: Histogram

Data (in its raw form) is a collection of numbers, characters, or observations that might seem overwhelming or meaningless. Describing data is the crucial step in unlocking its potential. In essence, describing data is like laying the groundwork for a building. It provides a clear understanding of the data’s characteristics, empowers informed decision-making, and paves the way for further analysis to extract valuable insights.

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Data View in SPSS (2024)

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The IBM SPSS has two main windows (i) Data View and (ii) Variable View. Data View in SPSS is one of the primary ways of looking at a data file in Data View so that you can see each row as a source of data and each column as a variable. The data view in SPSS is the most useful way to look at the actual values of the data presented in the data set.

By default, SPSS launches in Data View mode.

Data View in SPSS

The following diagram of the SPSS workplace highlights the data view in SPSS and the variable view in SPSS.

Data View in SPSS

If you are not in Data View, click the Data View Tab to enter the data view and the data edit mode. Typically, one should enter the data after establishing the names and other properties of the variables in a data set. Many of the features of Data View are similar to the features that are found in spreadsheet-like applications (such as MS Excel). There are, however, several important distinctions:

SPSS Data view
  • Rows are cases: Each row in a data view represents a case or an observation. For example, each respondent to a questionnaire is a case.
  • Columns are variables: Each column represents a variable or characteristic being measured. For example, each item on a questionnaire is a variable.
  • Cells contain values. The cross-section of the row and column makes a cell. Each cell contains a single value of a variable for a case. The cell is where the case and the variable intersect. Cells contain only data values. Unlike spreadsheet programs, cells in the Data Editor cannot contain formulas.

In summary, the Data View in SPSS is the primary workspace for viewing, manipulating, and understanding the actual values in the dataset. It plays a vital role in data exploration, cleaning, and analysis.

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Important MCQs Sampling and Sampling Distributions Quiz 10

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The MCQs on sampling Distribution Quiz is about the Basics of Sampling and Sampling Distributions. It will help you understand the basic concepts of sampling methods and distributions. These MCQs on sampling distribution tests will also help you prepare for different exams related to education or jobs. Most of the MCQs on Sampling Distribution, cover the topics of Probability Sampling and Non-Probability Sampling, Mean and Standard Deviation of Sample, Sample size, Sampling error, Sample bias, Sample Selection, etc.

Multiple Choice Questions about Sampling and Sampling Distributions with Answers

1. The sampling technique that selects every sixteenth person from a community is called

 
 
 
 

2. Sampling is used in situations

 
 
 
 

3. Which of the following is a type of non-probability sampling

 
 
 
 

4. Which of the following would generally require the largest sample size?

 
 
 
 

5. In stratified sampling, a sample drawn randomly from strata is classified as

 
 
 
 

6. Stratified sampling is a type of

 
 
 
 

7. Which of the following statements best describes the relationship between a parameter and a statistic?

 
 
 
 

8. In stratified random sampling with strata weights 0.35, 0.55, and 0.10, SD 16, 23, and 19, and sample sizes 70, 110, and 20, the variance of the sample mean estimator is?

 
 
 
 

9. Stratified sampling is a type of

 
 
 
 

10. An unbiased sample is representative of the population being measured. Which of the following helps ensure unbiased sampling?

 
 
 
 

11. In sampling with replacement, a sampling unit can be selected

 
 
 
 

12. Choose the sample size $n$ to be the same for all the strata is called

 
 
 
 

13. The standard deviation of a sampling distribution is called

 
 
 
 

14. Bias in which few respondents respond to the offered questionnaire is classified as

 
 
 
 

15. A group consists of 200 people and we are interviewing 60 members at random of a given group is called

 
 
 
 

16. In systematic sampling, the population of 200, and the selected sample size is 50 then the sampling interval is

 
 
 
 

17. To develop an interval estimate of any parameter of population value which is added or subtracted from point estimate is classified as

 
 
 
 

18. For sampling, which ONE of the following should be up-to-date, complete, and affordable?

 
 
 
 

19. In which of the following types of sampling the information is carried out under the opinion of an except?

 
 
 
 

20. Mrs. Tahir samples her class by selecting 5 girls and 7 boys. This type of sampling is called?

 
 
 
 

Sampling and Sampling Distributions Quiz with Answers

MCQs Sampling and Sampling Distributions Quiz with Answers

  • In stratified random sampling with strata weights 0.35, 0.55, and 0.10, SD 16, 23, and 19, and sample sizes 70, 110, and 20, the variance of the sample mean estimator is?
  • Stratified sampling is a type of
  • In stratified sampling, a sample drawn randomly from strata is classified as
  • Which of the following statements best describes the relationship between a parameter and a statistic?
  • The sampling technique that selects every sixteenth person from a community is called
  • In sampling with replacement, a sampling unit can be selected
  • The standard deviation of a sampling distribution is called
  • Choose the sample size $n$ to be the same for all the strata is called
  • Stratified sampling is a type of
  • Sampling is used in situations
  • In which of the following types of sampling the information is carried out under the opinion of an except?
  • For sampling, which ONE of the following should be up-to-date, complete, and affordable?
  • An unbiased sample is representative of the population being measured. Which of the following helps ensure unbiased sampling?
  • Bias in which few respondents respond to the offered questionnaire is classified as
  • In systematic sampling, the population of 200, and the selected sample size is 50 then the sampling interval is
  • To develop an interval estimate of any parameter of population value which is added or subtracted from point estimate is classified as
  • A group consists of 200 people and we are interviewing 60 members at random of a given group is called
  • Which of the following would generally require the largest sample size?
  • Mrs. Tahir samples her class by selecting 5 girls and 7 boys. This type of sampling is called?
  • Which of the following is a type of non-probability sampling

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Random Variables in Statistics

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In any experiment of chance, the outcomes occur randomly. For example, rolling a single die is an experiment: Any of the six possible outcomes can occur. Some experiments result in outcomes that are quantitative (such as dollars, weight, or number of children), and others result in qualitative outcomes (such as color or religious preferences). Therefore, random variables in statistics are variables whose value depends on the output of a random experiment.

A random variable is a mathematical abstraction that allows one to assign numerical values to the random variable associated with a probability to indicate the chance of a particular outcome.

Random Experiment

In the random experiment, a numerical value say 0, 1, 2, is assigned to each sample point. Such a numerical quantity whose value is determined by the outcomes of an experiment of chances is known as a random variable (or stochastic variable). Therefore, a random experiment is a process that has a well-defined set of possible outcomes, however, the outcomes for any given trial of the random experiment cannot be predicted in advance. Examples of random experiments are: rolling a die, flipping a coin, and measuring the height of students walking into a class.

Random Experiments: Random Variables in Statistics

Classification of Random Variables in Statistics

A random variable can be classified into a discrete random variable and a continuous random variable.

Discrete Random Variable

A discrete random variable can assume only a certain number of separated values. The discrete random variables can take only finite or countably infinite numbers of distinct values. For example, the Bank counts the number of credit cards carried by a group of customers. The other examples of discrete random variables are: (i) The number of successes in a 5-coin flip experiment, (ii) the number of customers arriving in a store during a specific hour, (iii) the number of students in a class, and (iv) the number of phone calls in a certain day.

Continuous Random Variable

The continuous random variable can assume any value within a specific interval. For example, the width of the room, the height of a person, the pressure in an automobile tire, or the CGPA obtained, etc. The continuous random variable assumes an infinitely large number of values, within certain limitations. For example, the tire pressure measured in pounds per square inch (psi) in most passenger cars might be 32.78psi, 31.32psi, 33.07psi, and so on (any value between 28 and 35). The random variable is the tire pressure, which is continuous in this case.

Definition: A random variable is a real-valued function that takes a defined value for every point in the sample space.

In most of the practical problems, discrete random variables represent count or enumeration data such as the number of books on a shelf, the number of cars crossing a bridge on a certain day or time, or the number of defective items in a production (or a lot). On the other hand, continuous random variables usually represent measurement data such as height, weight, distance, or temperature.

Note: A random variable represents the particular outcome of an experiment, while a probability distribution reports all the possible outcomes as well as the corresponding probability.

Types of Random Variable in Statistics

Importance of Random Variables

The importance of random variables cannot be ignored, because random variables are fundamental building blocks in the field of probability and statistics. The random variables allow us to:

  • Quantify Uncertainty: Since numerical values are assigned to outcomes from a random experiment, one can use mathematical tools such as probability distributions to compute and analyze the likelihood of different events occurring.
  • Statistical Analysis: Random variables are essential for performing various types of statistical analyses such as computing expected values, and variance, conducting hypothesis testing, and computing relationships between variables, etc.
  • Modeling Real-World Phenomena: One can use random variables to model real-world phenomena with inherent randomness, allowing for predictions and simulations.

Note that each possible outcome of a random experiment is called a sample point. The collection of all possible sample points is called sample space, represented by $S$.

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