Data analysis and interpretation is the process of assigning meaning to the collected information and determining the conclusions, significance, and implications of the findings. Data Interpretation can be called Comprehension of Mathematics. Data is given in the form of graphs, charts and tables followed by questions. We have to study, understand and analyse the data to solve the questions.
DATA: Data is a collection of facts, such as values or measurements. It can be numbers, words, measurements, observations or even just descriptions of things. Information refers to data being arranged and presented in a systematic or an organised form, so that some useful inferences can be drawn from the same. By data we generally mean quantities, figures, statistics, relating to any event.
What is DATA INTERPRETATION?
Data Interpretation is the extraction of maximum information from a given set of data or information. The data can be presented either in the form of a table or a bar chart or a pie chart or a line graph or as a combination of one of these formats.
Some Tips to solve DI questions:
The following tips may help in answering problem solving questions that involve Data Analysis.
* Before starting DI section one should be very comfortable with numbers, calculations, fractions, percentages, averages, ratios. It helps in reducing the time required for solving the questions. Scan the data briefly to see what it is about, but do not attempt to analyse it in too much detail before reading a question. Focus on only those aspects of the data that are necessary to answer the question.
* Read the data very carefully, as the smallest detail may change the meaning of the question completely. Similarly, the instructions have to be understood carefully to prevent wasting time in calculating data that is not required, and also to find out exactly what is the answer that is sought.
* When possible, try to make visual comparisons of the data given in a graph and estimate products and quotients rather than perform involved computations. Remember that these questions are to be answered only on the basis of the data given.
* Be very careful of the units used in the tables, and the units in which the answers (options) are provided. A mistake in the units may yield an entirely different answer.
* Also be careful of whether the answer is required in decimal or percentage. Such errors are common and easily avoidable. Let us see some of the graphs of various types.
BAR DIAGRAM
A bar diagram is that two dimensional graphic representation where the elementary graphic objects are a set of rectangles (bars) drawn in parallel so that the extension of the same is proportional to the magnitude they intend to represent.
* The rectangles, or bars, can be either horizontally or vertically positioned.
Simple Bar diagram:
If only one bar is given in the graph that is called simple bar diagram.
Ex: Following bar diagram gives the production of a company in various years.
1. What is the approximate average production of the company over the years?
1) 350 2) 420 3) 450 4) 380 5) 360
Sol: Average production
Hence answer is (4).
2. The production of the company in 2010 is how much percent more than the production in 2008?
1) 200% 2) 80% 3) 40% 4) 125% 5) None of these
Sol: Production in 2010 = 450
Production in 2008 = 250
=80%
Hence answer is (2).
Multiple Bar diagram:
When more than one adjacent vertical bars are given then that is called multiple bar diagram.
Ex: Following bar-diagram gives imports and exports of a country over the years.
1. The Exports in 2007-08 is what percent of the Exports in 2010-11?
1) 50% 2) 100% 3) 150% 4) 80% 5) None of these
Sol: Exports in 2007 − 08 = 300
Exports in 2010 − 11 = 200
Hence answer is (3).
2. The imports in 2008-09 are same as the exports in which of the following years?
1) 2006-07 2) 2010-11 3) 2008-09 4) 2009-10 5) None of these
Sol: From the graph we can observe that it is in 2006-07,
Hence answer is (1).
Sub-divided or component bar diagram:
Sub-divided or component bar chart is used to represent data in which the total magnitude (bar) is divided into different parts or components. In this diagram, first we make simple bars for each class taking total magnitude in that class and then divide these simple bars into parts in the ratio of various components.
Ex: Following graph gives the production of Computers by three companies A, B and C over the years. Production is in thousands.
1. What is the difference between the production of B in 1996 and 1999?
1) 17500 2) 20000 3) 15000 4) 25000 5) None of these
Sol: Production of B in 1996 is (55 − 20) = 35000
Production of B in 1999 is (30 − 10) = 20000
Difference = 35000 − 20000 = 15000
Hence answer is (3).
2. The production of C in 1994 is how much percent more than the production of A in 1997?
1) 25% 2) 12.5% 3) 22.4% 4) 16.67% 5) None of these
Sol: Production of C in 1994 is (60 − 40) = 20000
Production of A in 1997 is (15 − 0) = 15000
= 33.33%
Hence answer is (5)
LINE GRAPHS
A line graph is a type of graph, which displays information as a series of data points connected by straight line segments or A graph that uses points connected by lines to show how something changes in value.
Ex 1: Following line graph gives the production (in thousands) of a company over the years.
1. What is the difference between the highest and the lowest production of the company over the years?
1) 7500 2) 5000 3) 10000 4) 15000 5) None of these
Sol: Highest production = 8500
Lowest Production = 3500
Difference = 8500 − 3500 = 5000
Hence answer is (2).
2. In how many of the following years was the production of the company above the average?
1) 2 2) 4 3) 1 4) 5 5) None of these
Sol: Average production
Production is above average in three years
Hence answer is (5).
Ex 2: Following graph shows the profit (in lakhs) of two companies A and B over the years:
1. What is the difference between the average profit of the companies A and B over the years?
1) 2.5 lakh 2) 5 lakh 3) 4.75 lakh 4) 3.33 lakh 5) None of these
Sol: Average profit of A
Average profit of B
Difference in the average
Hence answer is (4).
