The post is about Online MCQs Basic Statistics with Answers. 20 Multiple-Choice questions covers the topics related to Tables, Frequency Distribution, Measures of Central Tendency, Measure of Dispersion, Coefficient of Variation, Skewness and Kurtosis, etc. Let us start with the Online MCQs Basic Statistics.
Online Multiple Choice Questions about Basic Statistics
Online MCQs Basic Statistics with Answers
If the third moment about mean is zero, the distribution is
The first moment about mean is
If $b_2=3$ then the distribution is
For moderately skewed distribution, the empirical formula holds
If $b_2 > 3$ the distribution is
The portion of the table containing row captions is called
The portion of the table containing column caption is called
Title of a table should be in
The difference between the upper and lower class boundary is called
Class Mark is also called
The frequency of the class divided by the total frequency is called
The sum of absolute deviations is minimum if these deviations are taken from
The measures of dispersion remains unchanged by the change of
The measures of dispersion are changed by the change of
The standard deviation is independent of change of
In Skewed distribution, approximately 95% of cases are falling between
If $\overline{x} = 8$ which of the following is minimum?
If $x=40$ and $S^2=64$ then the coefficient of variation is
The post is about Online MCQs Basic Statistics with Answers. There are 20 multiple-choice questions about variables, data, data classification, data types, measurable and non-measurable characteristics, frequency distribution, tables, and attributes. Let us start with the MCQS Basic Statistics with Answers.
The five number summary statistics is a set of descriptive statistics that summarizes a data set under study. Five number summary statistics consists of five numerical values that divide the data set into four equal parts. The five number summary statistics are also known as quartiles five number summary.
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Five Number Summary Statistics includes the following values:
Minimum Value: The smallest value in the data set.
First Quartile ($Q_1$): The value that separates the lowest 25% of the data from the remaining data sets.
Median ($Q_2$): The value that separates the lowest 50% from the highest 50% of the data.
Third Quartile ($Q_3$): The value that separates the lowest 75% of the data from the highest 25% of the data.
Maximum value: The largest value in the data set.
Visualization of Five Number Summary Statistics
A box plot can visually represent the five number summary statistics. The box plot displays the dataset’s range (Minimum and Maximum), the median ($Q_2$), and the quartiles ($Q_1$ and $Q_2$).
The Five number summary statistics is a useful way to quickly summarize: the central tendency, variability, and distribution of a data set.
Interquartile Range
The interquartile range (IQR) is a measure of variability that is based on the five number summary of a dataset. It is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$) of a data set. The rectangle in the box plot represents the interquartile range. The box represents the middle 50% of the data (between $Q_1$ and $Q_3$), with a line inside the box marking the median ($Q_2$).
What is a Box Plot
A box plot is a graphical representation of the five number summary statistics. It is also known as a box-and-whisker plot. It is used to see the distribution of the data and to detect outliers graphically/visually.
The relative positions of the quartiles and the median can provide clues about the shape of the distribution. For example, if the median is closer to $Q_1$, the distribution might be right-skewed. If the median is closer to $Q_3$, it might be left-skewed. If the median is roughly halfway between $Q_1$ and $Q_3$, the distribution might be roughly symmetric. The whiskers extend from the box to the minimum and maximum values, and sometimes outliers are plotted as individual points beyond the whiskers.
The five-number summary is a valuable tool for understanding the distribution of data and making comparisons between different datasets. It is often used in exploratory data analysis, quality control, and other statistical applications.
How to Compute the Five Number Summary Statistics:
First, arrange the data in ascending order.
Find the minimum and maximum values in the data set.
Find the median:
If the number of data points is odd, the median is the middlemost value in the sorted data.
If the number of data points is even, the median is the average of the two middlemost middle values of the sorted data.
Find $Q_1$ and $Q_3$:
$Q_1$ is the median of the lower half of the data (excluding the median if the number of data points is odd).
$Q_3$ is the median of the upper half of the data (excluding the median if the number of data points is odd).
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.
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Classification/ Presentation of Data in Statistics
The classification is a widely used data organization technique which is further classified into three categories
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
What is meant by the presentation of data?
What is the difference between tabulation, graphical presentation, and textual presentation of the data?
What are the different parts of a table? explain in detail.
Discuss different graphical representations.
Discuss the selection of the right method depending on the type of data.
What is the importance of tabulation in statistics?
