Data handling and Interpretation (charts, graphs, tables, data sufficiency etc.)

<–2/”>a >We have Bifurcated the topic Data handling and Interpretation (charts, graphs, tables, data sufficiency etc.) into following topics for exhaustive study:-

• Data Analysis – Mathematical operation Basic numeracy (numbers and their relations, orders of magnitude etc.)
• Data Interpretation (charts, graphs, tables, data sufficiency etc.) and analysis of data.
• Data Collection Analysis- Interpretation- Collection, Interpretat ion and Appreciation of Statistical Data
• Study of Graphs and Charts:– Bar Graphs, Line Graphs and Pie Charts-
• Problems Based on Tabular and Diagrammatical Data-
• Data Sufficiency In Statistics

Data interpretation

Data Interpretation or DI refers to the implementation of procedures through which data is reviewed for the purpose of arriving at an inference. Data can be obtained from multiple sources e.g. data from running of industries, census Population data etc. Interpreting data requires analyzing data to infer information from it in order to answer questions. Data can be provided in a number of formats viz: Bars, tables, line graphs, pie graphs.

Bar Graphs

A bar graph or bar chart represents explicit data with rectangular bars. The heights and lengths of these bar graphs are proportional to the values of data they represent. There are two types of bar graph, one is called horizontal bar graph and other is called vertical bar graph. The important thing to remember is that the longer the bar, the greater its value. Bar graphs made up of two axis, one is called x- axis and other is called y- axis. In a horizontal bar graph, y-axis shows the data categories and x- axis shows the scale. In vertical bar graph, x-axis shows the data categories and y-axis shows the scale. In a nutshell, we can compare easily different sets of data between different groups with the help of bar graph.

Tables

In tables, data is described in the form of rows and columns. In DI table’s questions, we are required to read data from table/tables analyze the data and answer the questions asked on the basis of the given data.

DI Questions based on Tables are very common in competitive exams. Rows and Columns of tables consist of various types of data like income of company, expenditure on various items, and marks of Applicants and so on. First column and row of tables represent the titles. Level of Questions in Tables may be lower or higher in comparison of other graphs form, depending on given data in the table and the way,questions are framed.

Line Graphs

A line graph basically is used to visualize values over a certain time period. It is basically used to change over time as various points of data connected by straight line on two axes. It helps to determine the relationship between two sets of values; and also one data set is always dependent on the other set. In many competitive exams, you will see various questions based on line chart problems, in which you are supposed to analyze the data and then answer them.

Pie Charts

Pie charts are circular shaped graphs which are divided into sectors to represent numerical proportions. In a pie chart, the central angle of a particular sector is proportional to the quantity it represents. In other words, we can say a Pie Chart resembles a Pie in which a circle is cut in various sized sectors from center to the boundary. In simple words, the bigger the sector, the higher the proportion.

Bar graphs

A Bar Graph (also called Bar Chart) is a graphical display of data using bars of different heights.

Imagine you just did a survey of your friends to find which kind of movie they liked best:

We can show that on a bar graph like this:

Pie charts

The formula to determine the angle of a sector in a circle graph is:

Angle  of sector = Frequency of data / Total frequency × 360°

Example:

Imagine you survey your friends to find the kind of movie they like best:

You can show the data by this Pie Chart:

It is a really good way to show relative sizes: it is easy to see which movie types are most liked, and which are least liked, at a glance.

Next, divide each value by the total and multiply by 100 to get a percent:

Now to figure out how many degrees for each “pie slice” (correctly called a sector).  A Full Circle has 360 degrees, so we do this calculation:

Data Sufficiency in Statistics

A sufficient statistic is a statistic that summarizes all of the information in a sample about a chosen parameter. For example, the sample mean, x̄, estimates the population mean, μ. x̄ is a sufficient statistic if it retains all of the information about the population mean that was contained in the original data points.

Let X1, X2, …, Xn be a random sample from a Probability distribution with unknown parameter θ. Then, the statistic:

Y=u(X1,X2,…,Xn)

is said to be sufficient for θ if the conditional distribution of X1, X2, …, Xn, given the statistic Y, does not depend on the parameter θ.

Guidelines to solve questions

In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer.

• If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
• If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
• If the data either in statement I alone or in statement II alone are sufficient to answer the question
• If the data given in both statements I and II together are not sufficient to answer the question and
• If the data in both statements I and II together are necessary to answer the question.

Example of Data sufficiency

Question: In which year was Rahul born ?

Statements:

1. Rahul at present is 25 years younger to his mother.
2. Rahul’s brother, who was born in 1964, is 35 years younger to his mother.

Answer  E

Explanation:

From both I and II, we find that Rahul is (35 – 25) = 10 years older than his brother, who was born in 1964. So, Rahul was born in 1954.

Pie-chart

A pie graph (or pie chart) is a specialized graph used in statistics. The independent variable is plotted around a circle in either a clockwise direction or a counterclockwise direction.The dependent variable (usually a Percentage) is rendered as an arc whose measure is proportional to the magnitude of the quantity.Each arc is depicted by constructing radial lines from its ends to the center of the circle, creating a wedge-shaped “slice.”The independent variable can attain a finite number of discrete values (for example, five).The dependent variable can attain any value from zero to 100 percent.

The illustration is a pie graph depicting the results of a final exam given to a hypothetical class of students.Each grade is denoted by a “slice.”The total of the percentages is equal to 100 (this is important; if it were not, the accuracy of the graph would be suspect).The total of the arc measures is equal to 360 degrees.

From this graph, one might gather that the professor for this course was not especially lenient nor severe.It is evident that grading was not done on a “pure curve” (in which case all the arcs would have equal measures of 72 degrees, corresponding to 20%).If this graph were compared with those of classes from other years that received the same test from the same professor, some conclusions might be drawn about intelligence changes among students over the years.If this graph were compared with those of other classes in the same semester who had received the same final exam but who had taken the course from different professors, one might draw conclusions about the relative competence and/or grading whims of the professors.

Example

Imagine you survey your friends to find the kind of movie they like best:

Pie chart representation of above table

Probability

Probability is simply how likely something is to happen.

Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Tossing a Coin

When a coin is tossed, there are two possible outcomes:

heads (H) or tails (T)

We say that the probability of the coin landing H is ½  And the probability of the coin landing T is ½.

Throwing Dice

When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6.

The probability of any one of them is  16

Number of ways it can happen

Probability of an event happening     =     ________________________

Total number of outcomes

 ,

Data handling and interpretation is a complex process that involves many different steps. In this ARTICLE, we will discuss the key steps involved in data handling and interpretation, as well as some of the challenges that can arise.

The first step in data handling is to collect the data. This can be done in a variety of ways, such as through surveys, interviews, or observation. Once the data has been collected, it needs to be organized. This can be done by creating a Database or spreadsheet.

The next step is to analyze the data. This involves looking for patterns and trends in the data. Data analysis can be done using a variety of statistical methods.

Once the data has been analyzed, it needs to be interpreted. This involves explaining the meaning of the data and drawing conclusions from it. Data interpretation can be done by creating graphs, charts, or other visual representations of the data.

The final step in data handling and interpretation is to communicate the results. This can be done through a variety of means, such as writing a report, giving a presentation, or creating a website.

Data handling and interpretation is a complex process, but it is essential for making informed decisions. By following the steps outlined in this article, you can ensure that your data is handled and interpreted in a way that is accurate and meaningful.

One of the challenges that can arise in data handling and interpretation is data bias. Data bias occurs when the data is not representative of the population that it is supposed to represent. This can happen for a variety of reasons, such as sampling error or non-response bias.

Another challenge that can arise in data handling and interpretation is data quality. Data quality refers to the accuracy, completeness, and consistency of the data. Data quality is important because it affects the reliability of the results of the data analysis.

Data handling and interpretation is a complex process, but it is essential for making informed decisions. By following the steps outlined in this article, you can ensure that your data is handled and interpreted in a way that is accurate and meaningful.

Here are some frequently asked questions and short answers about data handling and interpretation:

• What is data handling?
  Data handling is the process of collecting, organizing, and storing data. It is the first step in the data analysis process.

• What is data interpretation?
  Data interpretation is the process of making sense of data. It involves understanding the meaning of the data and drawing conclusions from it.

• What are the different types of data?
  Data can be classified into two types: quantitative and qualitative. Quantitative data is numerical data, such as the number of people in a population. Qualitative data is non-numerical data, such as the color of a person’s eyes.

• What are the different ways to handle data?
  Data can be handled in a variety of ways, depending on the type of data and the purpose of the analysis. Some common methods of data handling include data entry, data cleaning, data transformation, and data analysis.

• What are the different ways to interpret data?
  Data can be interpreted in a variety of ways, depending on the type of data and the purpose of the analysis. Some common methods of data interpretation include data visualization, data mining, and data modeling.

• What are the benefits of data handling and interpretation?
  Data handling and interpretation are essential for making informed decisions. By understanding the data, you can identify trends, patterns, and relationships. This information can be used to improve your business, make better products, and provide better Services.

• What are the challenges of data handling and interpretation?
  Data handling and interpretation can be challenging, especially if you are not familiar with the data or the analysis methods. It is important to have a good understanding of the data and the purpose of the analysis before you begin.

• What are some tips for data handling and interpretation?
  Here are some tips for data handling and interpretation:

• Be familiar with the data. Make sure you understand the type of data, the source of the data, and the limitations of the data.

• Have a clear purpose for the analysis. What do you hope to learn from the data?
• Choose the right analysis methods. There are many different methods for data analysis, so choose the methods that are appropriate for your data and your purpose.
• Be careful with your assumptions. Make sure you are not making any assumptions about the data that are not supported by the evidence.
• Be aware of your biases. We all have biases, so be aware of your own biases and how they might affect your interpretation of the data.
• Be open to new ideas. The data might lead you to new ideas, so be open to changing your mind about what you thought you knew.
• Communicate your results. Once you have analyzed the data, communicate your results to others in a clear and concise way.

I hope this helps! Let me know if you have any other questions.

Sure. Here are some multiple choice questions without mentioning the topic Data handling and Interpretation (charts, graphs, tables, data sufficiency etc.):

1. A survey of 1000 people found that 60% of them prefer chocolate ice cream to vanilla ice cream. What is the probability that a randomly selected person prefers chocolate ice cream?
   (A) 0.6
   (B) 0.4
   (C) 0.5
   (D) 0.3

2. A coin is tossed 10 times. What is the probability of getting 6 heads?
   (A) 1/1024
   (B) 1/100
   (C) 1/256
   (D) 1/64

3. A bag contains 5 red balls, 3 green balls, and 2 blue balls. What is the probability of drawing a red ball?
   (A) 5/10
   (B) 3/10
   (C) 2/10
   (D) 1/10

4. A box contains 10 balls, of which 6 are red and 4 are blue. Two balls are drawn without replacement. What is the probability that both balls are red?
   (A) 1/15
   (B) 1/10
   (C) 1/3
   (D) 1/2

5. A fair die is rolled. What is the probability of getting a number greater than 3?
   (A) 1/2
   (B) 1/3
   (C) 2/3
   (D) 1/6

6. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a heart?
   (A) 1/2
   (B) 1/4
   (C) 1/3
   (D) 1/13

7. A coin is tossed 3 times. What is the probability of getting 2 heads and 1 tail?
   (A) 1/8
   (B) 3/8
   (C) 5/8
   (D) 7/8

8. A bag contains 5 red balls, 3 green balls, and 2 blue balls. Two balls are drawn without replacement. What is the probability that one ball is red and one ball is green?
   (A) 1/10
   (B) 3/10
   (C) 6/10
   (D) 9/10

9. A fair die is rolled 6 times. What is the probability of getting at least one 6?
   (A) 1/6
   (B) 5/6
   (C) 11/36
   (D) 25/36

10. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a spade or a heart?
    (A) 1/2
    (B) 1/4
    (C) 1/3
    (D) 1/13

I hope these questions are helpful! Let me know if you have any other questions.