Basic Statistics

Since the primary data is in raw form or haphazard, it is not easy to examine the unorganized data. The scientist or researcher has organized the data in an understandable and meaningful way. In this post, we will learn about the organization/ presentation of data in Statistics. The presentation of data in statistics is a vital aspect, as it transforms raw data into meaningful and understandable information.

Classification/ Presentation of Data in Statistics

The classification is a widely used data organization technique which is further classified into three categories

• Tabulation (Frequency Distribution and Contingency Tables)
• Graphical Presentation of Data (Bar charts, Pie charts, scatter diagrams. line charts, etc.)
• Textual Presentation of Data (Descriptive Statistics)

Classification of Data

Classification is defined as the process of dividing a set of data into different groups or categories so that they are homogeneous with respect to their characteristics and mutually exclusive. In other words, classification is a method that divides a set of data into different heterogeneous groups or sorts the data into different heterogeneous groups, by sort we mean a systematic arrangement of objects, individuals, and units in such a way that different categories are created.

The data can be classified/presented/organized in different ways, such as color classification, age classification, gender classification, and grade classification.

Tabulation

The classification of data in tabular form with suitable headings of tables, rows, and columns is called tabulation. There are different parts or components of a table: (i) Title, (ii) Column Caption, (iii) Row Caption, (iv) Footnotes, (v) Source note.

• Table Number: A number is allocated to the table for identification, particularly when there are a lot of tables in the study.
• Title: The title of the table should explain what is contained in the table. The title must be concise, clear, brief, and set in bold type font on the top of the table. It may also indicate the time and place to which the data refer.
• Stub or Row Designations: Each row of the table should be given a brief heading called stubs or stub items. For columns, it is called the stub column.
• Column Headings or Captions: column designation is given on top of each column to explain to what the figures in the column refer. It should be concise, clear, and precise. This is called caption, or heading. Columns can also be numbered if there are four or more columns in a table.
• Body of the Table: The data should be organized/ arranged in such a way that any data point/ figure can be located easily. Various types of numerical variables should be arranged in ascending order from left to right in rows and from top to bottom in columns. The columns and rows totals can also be given.
• Source: At the bottom of the table, a note should be added indicating the primary and secondary sources from which data have been collected
• Footnotes and references: If any item has not been explained properly, a separate explanatory note should be added at the bottom of the table.

Importance of Tabulation

In Tabulation, data are arranged and it makes data brief.

• In tabulation, data is divided into various parts and for each part, there are totals and sub totals. Therefore, relationships between different parts can easily be established.
• Since data is organized in a table with a title and a number, data can be easily identified and used for the required purpose.
• Tables can be easily presented in the form of graphs.
• Tabulations make complex data simple making it easy to understand the data.
• Tabulation also helps in identifying mistakes and errors.
• Tabulation condenses the collected data and it becomes easy to analyze the data from tables.
• Tabulation saves time and costs as it is the easiest and most comprehensive method used to organize the data.
• Since tabulation summaries, the large scattered data, the maximum information may be gained/collected from these tables.

Limitations of Tabulation

• Tables contain only numerical data. The tables do not contain further details.
• Qualitative expressions are not possible through tables.
• Usually, tables are used by experts to conclude, but common men cannot understand them properly.

Examples of Tabulation

Consider, that a district is divided into two areas urban area and rural area, The Total population of the district is 271076 out of which only 46740 live in the urban area. The total male population of the district is 139699 and that of the urban area is 23083. The total unmarried population of the district is 112352 out of which 36864 are rural females. In the urban area unmarried people number 21072 out of which 12149 are males. Construct a table showing the population of the district by marital status, residence, and Gender.

Graphical Presentation of Data In Statistics

Visualization or Graphical presentation of data in statistics helps researchers visualize hidden information in a graphical/visual way. There are many types of graphical representations of the data:

• Bar Charts: Bar charts are used to represent the frequency, percentage, or magnitude of different categories or groups in rectangular form. Simple bar charts are used to compare different categories while multiple bar charts are used to compare multiple categories over time or across groups. The stacked bar charts are used to show the composition of each category.
• Pie Charts: Pie charts are used to represent the proportions of a whole as slices/sectors of a pie.
• Line Graphs: Line graphs are used to show trends over time or relationships between variables.
• Scatter plots: Scatter plots are used to visualize the relationship between two quantitative variables.
• Histogram: Histograms are similar to bar charts where the bars are adjacent, representing the frequency distribution of a continuous variable.

Textual Presentation of Data in Statistics

Textual presentation of data includes descriptive statistics. Descriptive statistics summarizes the data using numerical measures like mean, median, mode, range, and standard deviation.

Selection of the Right Method for the Presentation of Data

For the presentation of data in statistics, one should be careful in selecting the right method of data representation. The selection or choice of the right method depends on:

• Type of data: The visualization or textual presentation of data depends on the type of the data. For example, categorical data (such as gender, color, etc.) is often presented using bar charts or pie charts, while numerical data (such as age, marks, income, etc.) is better suited for histograms, line graphs, or scatter plots.
• Purpose: To show the trends of data over time, one can use a line graph. A pie chart is suitable for comparing proportions. Therefore, the selection of presentation of data depends on the purpose, use, or application of data in real life.
• Audience: The selection of different presentations of data depends on the familiarity of the audience with different types of graphs and charts. Simpler visualizations might be more effective for a general audience.

FAQS about Presentation of Data in Statistics

1. What is meant by the presentation of data?
2. What is the difference between tabulation, graphical presentation, and textual presentation of the data?
3. What are the different parts of a table? explain in detail.
4. Discuss different graphical representations.
5. Discuss the selection of the right method depending on the type of data.
6. What is the importance of tabulation in statistics?

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This post is about Basic Statistics MCQs with Answers. There are 20 multiple-choice questions from the construction of frequency distribution, cumulative frequency, class intervals, class boundaries, and class width. Let us start with Basic Statistics MCQs with Answers.

Basic Statistics MCQs with Answers

• The classification method in which the upper and lower limits of the interval are also in the class interval itself is called
• General tables of data used to show data in an orderly manner are called as
• Frequencies of all specific values of x and y variables with total calculated frequencies are classified as
• A term used to describe frequency curve is
• Distribution which shows a cumulative figure of all observations placed below the upper limit of classes in distribution is considered as
• A distribution which requires the inclusion of open-ended classes is considered as
• The type of cumulative frequency distribution in which class intervals are added in bottom-to-top order is classified as
• The ‘less than type distribution’ and ‘more than type distribution’ are types of
• The exclusive method and inclusive method are ways of classifying data on the basis of
• The type of classification in which a class is subdivided into subclasses and subclasses are divided into more classes is considered as
• Frequency distribution which is the result of cross-classification is called
• The type of table in which study variables provide a large number of information with interrelated characteristics is classified as
• Table in which data represented is extracted from some other data table is classified as
• The class interval classification method which ensures data continuity is classified as
• Which one of the following is the class frequency?
• A complex type of table in which variables to be studied are subdivided with interrelated characteristics is called as
• ‘less than type’ cumulative frequency distribution is considered as correspondence to
• The type of classification in which a class is subdivided into subclasses and one attribute is assigned for statistical study is considered as
• Cumulative frequency distribution which is the ‘greater than’ type is correspondent to
• Simple classification and manifold classification are types of

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The post is about MCQs Data and Variables. There are 20 multiple-choice questions related to variables, data, population, sample, and types of variables. Let us start with MCQs Data and Variable with Answers.

Please go to MCQs Data and Variable 14 to view the test

MCQs Data and Variable with Answers

• When data are collected in a statistical study for only a portion or subset of all elements of interest we are using:
• In statistics, a population consists of:
• In statistics, a sample means:
• In statistics, conducting a survey means:
• A data set is a:
• A variable is a:
• An observation is the:
• A quantitative variable is one that can:
• A qualitative variable is the one that:
• Time-series data are collected:
• Cross-section data are collected:
• Which one of the following is an example of qualitative data?
• Which one of the following is an example of cross-section data?
• Which one of the following is a continuous variable?
• What tasks are involved in data cleaning? Select all that apply
• What is the main objective of data cleaning?
• A statistician wants to determine the total annual medical costs incurred by all districts of Pakistan from 1981 to 2001 as a result of health problems related to smoking. He polls each of the districts annually to obtain health care expenditures, in dollars, on smoking-related illnesses. Which one of the following is not a true statement?
• A scientist is experimenting to determine the relationship between the consumption of a certain type of food and high blood pressure. He conducts a random sample on 2,000 people and first asks them a “yes” or “no” question: Do you eat this type of food more than once a week? He also takes the blood pressure of each person and records it (for example: 120/80). Which one of the following statements is true?
• Variables whose measurement is done in terms such as weight, height, and length are classified as
• Government and non-government publications are considered as

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To learn about errors in statistics, we first need to understand the concepts related to true value, accuracy, and precision. Let us start with these basic concepts.

True Value

The true value is the value that would be obtained if no errors were made in any way by obtaining the information or computing the characteristics of the population under study.

The true value of the population is possible obtained only if the exact procedures are used for collecting the correct data, every element of the population has been covered and no mistake or even the slightest negligence has happened during the data collection process and its analysis. It is usually regarded as an unknown constant.

Accuracy

Accuracy refers to the difference between the sample result and the true value. The smaller the difference the greater will be the accuracy. Accuracy can be increased by

• Elimination of technical errors
• Increasing the sample size

Precision

Precision refers to how closely we can reproduce, from a sample, the results that would be obtained if a complete count (census) was taken using the same method of measurement.

Errors in Statistics

The difference between an estimated value and the population’s true value is called an error. Since a sample estimate is used to describe a characteristic of a population, a sample being only a part of the population cannot provide a perfect representation of the population (no matter how carefully the sample is selected). Generally, it is seen that an estimate is rarely equal to the true value and we may think about how close will the sample estimate be to the population’s true value. There are two kinds of errors, sampling and non-sampling errors.

• Sampling error (random error)
• Non-sampling errors (nonrandom errors)

Sampling Errors

A sampling error is the difference between the value of a statistic obtained from an observed random sample and the value of the corresponding population parameter being estimated. Sampling errors occur due to the natural variability between samples. Let $T$ be the sample statistic and it is used to estimate the population parameter $\theta$. The sampling error may be denoted by $E$,

$$E=T-\theta$$

The value of the sampling error reveals the precision of the estimate. The smaller the sampling error, the greater will be the precision of the estimate. The sampling error may be reduced by some of the following listed:

• By increasing the sample size
• By improving the sampling design
• By using the supplementary information

Usually, sampling error arises when a sample is selected from a larger population to make inferences about the whole population.

Non-Sampling Errors

The errors that are caused by sampling the wrong population of interest and by response bias as well as those made by an investigator in collecting, analyzing, and reporting data are all classified as non-sampling errors (or non-random errors). These errors are present in a complete census as well as in a sampling survey.

Bias

Bias is the difference between the expected value of a statistic and the true value of the parameter being estimated. Let $T$ be the sample statistic used to estimate the population parameter $\theta$, then the amount of bias is

$$Bias = E(T) – \theta$$

The bias is positive if $E(T)>\theta$, bias is negative if $E(T) <\theta$, and bias is zero if $E(T)=\theta$. The bias is a systematic component of error that refers to the long-run tendency of the sample statistic to differ from the parameter in a particular direction. Bias is cumulative and increases with the increase in size of the sample. If proper methods of selection of units in a sample are not followed, the sample result will not be free from bias.

Note that non-sampling errors can be difficult to identify and quantify, therefore, the presence of non-sampling errors can significantly impact the accuracy of statistical results. By understanding and addressing these errors, researchers can improve the reliability and validity of their statistical findings.

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