Data Analysis & Interpretation -PO

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Last updated: July 17, 2018

Data Interpretation

Data Interpretation is an important part of all the bank exams. It is a separate section in SBI PO and IBPS PO exams.

Data interpretation refers to the process of critiquing and determining the significance of important information, such as survey results, experimental findings, observations or narrative reports. Interpreting data is an important critical thinking skill that helps you comprehend text books, graphs and tables. Researchers use a similar but more meticulous process to gather, analyze and interpret data. Experimental scientists base their interpretations largely on objective data and statistical calculations. Social scientists interpret the results of written reports that are rich in descriptive detail but may be devoid of mathematical calculations.

Why Data Interpretation?

Why is there Data Interpretation in bank exams?  Why is this important?  Well, do you know the old adage “A picture is worth a thousand words“?  Well, a graph is worth even more.  Geeky math & techie folks, such as I, absolutely love graphs and charts, because they present an efficient means to convey a truckload of information in way that is directly visually accessible.  In our post-modern electronic world, the sheer amount of information available is simply mind-boggling.  Graphs and charts are essential for keeping track of all this information.

Here’s one big suggestion for  Data Interpretation: if you are not a geeky math or techie person, start looking at graphs & charts.  Look in the financial news, in scientific articles, and in international news in general.    Spend time studying them: each graph, each chart, has a “story” to tell.  Spend enough time with each to understand its “story.”

What You Need to Know for  Data Interpretation

Data Interpretation will present information in any one of a number of visual formats.  These include:

(a) pie charts

(b) bar charts

(c) line graphs

(d) Multi graph

(e) Data Sufficiency

(f) Tables

Table Chart

Study the following table and answer the questions based on it.

Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.

Year Item of Expenditure
Salary Fuel and Transport Bonus Interest on Loans Taxes
1998 288 98 3.00 23.4 83
1999 342 112 2.52 32.5 108
2000 324 101 3.84 41.6 74
2001 336 133 3.68 36.4 88
2002 420 142 3.96 49.4 98

Question 1 :

The total amount of bonus paid by the company during the given period is approximately what percent of the total amount of salary paid during this period?

A. 0.1%

B. 0.5%

C. 1%

D. 1.25%

Answer : Option C

Explanation:

Required Percentage =    \left [ \frac{(3.00 + 2.52 + 3.84 + 3.68 + 3.96 )}{(288 + 342 + 324 + 336 + 420)}\times\! 100 \right] %

=  \left [ \frac{17 }{1710}\times\! 100 \right] %

 \approx1%

Question 2 :

Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002?

A. 62%

B. 66%

C. 69%

D. 71%

Answer : Option C

Explanation:

Required Percentage =     \left [ \frac{(288 + 98 + 3.00 +23.4 + 83 )}{(420 + 142 + 3.96 + 49.4 +98)}\times\! 100 \right] %

  \left [ \frac{17 }{1710}\times\! 100 \right] %

=  \left [ \frac{495.4 }{713.36}\times\! 100 \right] %

 \approx69.45%

Question 3 :

The total expenditure of the company over these items during the year 2000 is?

A.  Rs.  544.44 lakhs

B.  Rs.  501.11 lakhs

C.  Rs.  446.46 lakhs

D.  Rs.  478.87 lakhs

Answer : Option A

Explanation:

Total expenditure of company during 2000

= Rs. (324 + 101+ 3.84 + 41.6 + 74) lakhs

= Rs. 544.44 lakhs.

Bar Graph

Bar graph is a type of graph in which the values are represented in the form of stacks or bars.

These bars or stacks can represent one or more series in the same graph. A bar graph may be either horizontal or vertical. To differentiate between the two, a vertical bar graph is called a column graph. An important point about bar graphs is that the length of the graph is proportional to its value: the greater the length, the greater the value.

Example 1 Bar Graph

Bar Graph

The category axis or the x-axis shows the categories being compared and the y-axis shows a discrete value corresponding to each category. Some bar graphs show data in clustered groups over a period and in others, the bar is divided into smaller parts to show cumulative effect. The latter kind of bar graphs are called stack graphs.

Components Of A Bar Graph

A bar graph has the following components.

Chart Title:

It is present at the top of the graph and indicates what is graph is about. In the given graph, the chart title is ‘Internet use at Redwood Secondary School, number of students I.e, boys and girls year wise break up.’

Components Of A Bar Graph

Axes:

These are the two perpendicular lines labeled like number lines. The horizontal axis is called the X-axis. The vertical axis is called the  Y-axis.

Both the axes contain labels that are used to read the values. In the preceding graph, title X-axis has year wise breakup while the Y axis has number of students using internet as labels.

Axes titles:

these are the titles of the axes. In the given graph, the x-axis title is ‘Years’ and the y-axis title is ‘number of students’.

Components Of A Bar Graph

Grid Lines:

these are the lines that extend from horizontal or vertical axes across the plot area of the chart. They improve the readability of the graph.

Grid lines are of two types:

I)Major grid lines: these are the grid lines marked parallel to the labels.

II)Minor gridlines: these are the thinner gridlines between the major grid lines.

Legend:

data are represented by multiple colours or textures. Legend explains what a particular colour or texture represents. In the below graph, the legend tells us that boys are represented by orange while girls are represented by yellow colour.

How To Read A Bar Graph?

A bar graph is read using the gridlines. Observe the tip of the graph.
Value of bar = value or preceding major gridline + N x width of minor gridline where N represents the number of the minor gridline which touches the bar. Let’s take the above graph. Here the width of a major gridline is 5 and there are 5 minor gridlines between two successive major gridlines. Hence the width of minor gridline = 1 suppose we have to calculate the number of boys in section A the preceding major gridline 1ast 30. There are 2 minor gridlines are that. Hence the value is 30 + 2 = 32.

Types Of Bar Graph?

Bar Graphs are of two types :

Vertical Bar Graph:

Also called column graph. In these graphs, the X-axis shows the categories being compared and the Y-axis shows a discrete value corresponding to each category.

Horizontal Bar Graph:

It is the axis reversal of the vertical graph. In these graphs, the Y-axis shows the categories and the X-axis shows the value corresponding to the category.

Vertical Bar Graph

Horizontal Bar Graph

Stack Bar Graph

A stacked bar graph represents data sets on top of each other. The height of the resulting bar shows the combined result of the data sets. However, stacked bar charts are not suited to data sets where some groups have negative values.

Stack Bar Graph

Bar Chart

The bar graph given below shows the sales of books (in thousand number) from six branches of a publishing company during two consecutive years 2000 and 2001.

Sales of Books (in thousand numbers) from Six Branches – B1, B2, B3, B4, B5 and B6 of a publishing Company in 2000 and 2001.

Question 1 :

What is the ratio of the total sales of branch B2 for both years to the total sales of branch B4 for both years?

A.  2: 3

B.  3 : 5

C.  4 : 5

D.  7 : 9

Answer : Option D

Explanation:

Required ratio = \frac{75 + 65}{85 + 95}  \frac{140}{180}  \frac{7}{9}

Question 2 :

Total sales of branch B6 for both the years is what percent of the total sales of branches B3 for both the years?

A.  68.54%

B.  71.11%

C.  73.17%

D. 75.55%

Answer : Option C

Explanation:

Required Percentage =    \left [ \frac{(70 + 80 )}{(95+ 110 )}\times\! 100 \right] %

  \left [ \frac{150 )}{205}\times\! 100 \right] %

=73.17 %

Question 3 :

What percent of the average sales of branches B1, B2 and B3 in 2001 is the average sales of branches B1, B3 and B6 in 2000?

A.  75%

B.  77.5%

C.  82.5%

D.  87.5%

Answer : Option D

Explanation:

Average sales ( in thousand number ) of branches B1, B3 and B6 in 2000 .

=  \frac{1}{3}\times\!(80 + 95 + 70) \frac{245}{3}\

Average sales ( in thousand number ) ofbranches B1, B2 and B3 in 2001

= \frac{1}{3}\times \! (105 + 65 + 110) \frac{280}{3}\

Required percentage = \left [ \frac{245/3}{280/3}\times\! 100 \right]

=   \left [ \frac{245}{280}\times\! 100 \right]

=87.5%

Question 4 :

What is the average sales of all the branches (in thousand numbers) for the year 2000?

A.  73

B.  80

C.  83

D.  88

Answer : Option B

Explanation:

Average sales of all the six branches ( in thousand numbers) for the year 2000

 \frac{1}{6} \times  [80 + 75 + 95 +85 + 75 + 70]

= 80

Question 5 :

Total sales of branches B1, B3 and B5 together for both the years (in thousand numbers) is?

A.  250

B.  310

C.  435

D.  560

Answer : Option D

Explanation:

Total sales of branches B1, B3 and B5 for both the years ( in thousand numbers)

= (80 + 105 ) + ( 95 +110) + (75 + 95)

=560

Pie Chart

The following pie-chart shows the percentage distribution of the expenditure incurred in publishing a book. Study the pie-chart and the answer the questions based on it.

Various Expenditures (in percentage) Incurred in Publishing a Book

Question 1 :

If for a certain quantity of books, the publisher has to pay Rs. 30,600 as printing cost, then what will be amount of royalty to be paid for these books?

A.  Rs.  19,450

B.  Rs.  21,200

C.  Rs.  22,950

D.  Rs.  26,150

Answer : Option C

Explanation:

Let the amount of Royalty to be paid for these books be Rs r.

Then , 20 : 15 = 30600 :r => r = Rs.   ( \frac{30600\times\!15}{20}  ) = Rs 22,950.

Question 2 :

What is the central angle of the sector corresponding to the expenditure incurred on Royalty?

A. 150

B. 240

C. 540

D. 480

Answer :Option C

Explanation

Central angle corresponding to Royalty ( 15 % of 3600)

  ( \frac{15}{100}\times\!360 )0

= 540

Question 3 :

The price of the book is marked 20% above the C.P. If the marked price of the book is Rs. 180, then what is the cost of the paper used in a single copy of the book?

A. Rs. 36

B. Rs. 37.50

C. Rs 42

D. rs. 44.25

Answer :Option B

Explanation

Clearly marked price of the book = 120% of C.P.

Also cost of paper = 25% of C.P

Let the cost of paper for a single book be Rs. n.

Then 120 :25 = 180 : n => n = Rs.    ( \frac{25}{180}\times\!120 )

= Rs 37.50

Question 4 :

If  5500 copies are published and the transportation cost on them amounts to Rs. 82500, then what should be the selling price of the book so that the publisher can earn a profit of 25%?

A. Rs . 187.50

B. Rs . 191.50

C. Rs . 175.50

D. Rs . 180

Answer :Option A

Explanation

For the publisher to earn a profit of 25%, S.P. = 125% of C. P.

Also Transportation Cost = 10% of C. P.

Let the s.P. of 5500 books be Rs. x.

Then, 10 : 125 = 82500 : x  => Rs.  ( \frac{125 \times\! 82500}{10} )

= Rs 10,31,250

so S.P of one book = Rs  ( \frac{ 10,31,250}{5,500} )

=Rs 187.50.

Question 5 :

Royalty on the book is less than the printing cost by

A. 5%

B. 33  ( \frac{1}{5} )%

C. 20%

D. 25%

Answer :Option A

Explanation

Pricing cost of book = 20% of C.P.

Royalty on book = 155 of C.P.

Difference = ( 20 % of C.P) – (15% of C.P ) = 5% of C.P.

So percentage difference =   ( \frac{Difference }{Printing \: cost}\times\! 100 )%

  ( \frac{5 \% \of \ CP }{Printing \: cost}\times\! 100 )% = 25%.

Line  Chart

Study the following line graph and answer the questions.

Exports from Three Companies Over the Years (in Rs. crore)

Question 1 :

For which of the following pairs of years the total exports from the three Companies together are equal?

A.  1995 and 1998
B.  1996 and 1998
C.  1997 and 1998
D.  1998 and 1996
Answer : Option D
Explanation:
Total exports of the three companies X, Y and Z together during various year are :
In 1993 = Rs. (30 + 80 + 60 ) crores = Rs. 170 crores.
In 1994 = Rs. (60 + 40 + 90 ) crores = Rs. 190 crores.
In 1995 = Rs. (40 + 60 + 120 ) crores = Rs. 220 crores.
In 1996 = Rs. (70 + 60 + 90 ) crores = Rs. 220 crores.
In 1997 = Rs. (100 + 80 + 60 ) crores = Rs. 240 crores.
In 1998 = Rs. (50 + 100 + 80 ) crores = Rs. 230 crores.
In 1999 = Rs. (120 + 140 + 100 ) crores = Rs. 360 crores.
Clearly the total exports of the three companies X, Y and Z together are same during the years 1995 and 1996.

Question 2 :

Average annual exports during the given period for Company Y is approximately what percent of the average annual exports for Company Z?

A.  87.12%
B.  89.64%
C.  91.21%
D.  93.33%
Answer : Option D

Explanation:

The amount of exports of Company X (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 30, 60, 40, 70, 100, 50 and 120 respectively.

The amount of exports of Company Y (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 80, 40, 60, 60, 80, 100 and 140 respectively.

The amount of exports of Company Z (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 60, 90,, 120, 90, 60, 80 and 100 respectively.

Average annual exports (in Rs. crore) of Company Y during the given period

  = \frac{1}{7} \times \!(80 +40 +60 + 60 +80 + 100 + 140) = \frac{560}{7} = 80

Average annual exports (in Rs. crore) of Company Z during the given period

  = \frac{1}{7} \times \!(60 +90 +120 + 90 + 60 +80 + 100) = \frac{600}{7}
Required Percentage =  [\frac{80}{\frac{600}{7}} \times \! 100 \right ]] % = 99.33%

Question 3 :

In which year was the difference between the exports from Companies X and Y the minimum?

A.   1994
B.   1995
C.   1996
D.   1997
Answer : Option D

Explanation:

The difference between the exports from the Companies X and Y during the various years are:

In 1993 = Rs. (80 – 30) crores = Rs. 50 crores.

In 1994 = Rs. (60 – 40) crores = Rs. 20 crores.

In 1995 = Rs. (60 – 40) crores = Rs. 20 crores.

In 1996 = Rs. (70 – 60) crores = Rs. 10 crores.

In 1997 = Rs. (100 – 80) crores = Rs. 20 crores.

In 1998 = Rs. (100 – 50) crores = Rs. 50 crores.

In 1999 = Rs. (140 – 120) crores = Rs. 20 crores.

Clearly, the difference is minimum in the year 1996.

Q4. What was the difference between the average exports of the three Companies in 1993 and the average exports in 1998?

A.   Rs 15.33 crores
B.   Rs 18.67 crores
C.   Rs 20 crores
D.  Rs 22.17 crores
Answer : Option C

Explanation:

Average exports of the three Companies X, Y and Z in 1993
= Rs.[    \frac{1}{3} \times \!(30 +80 +60 ) ] crores =  Rs   ( \frac{170}{3})  crores
Average exports of the three Companies X, Y and Z in 1998
= Rs.[    \frac{1}{3} \times \!(50 +100 +80 ) ] crores =  Rs   ( \frac{230}{3})  crores

Difference =  Rs[   ( \frac{230}{3} ) - ( \frac{170}{3} ) ]crores

= Rs [   ( \frac{60}{3} )  ]crores

= Rs 20 crores

Q5.In how many of the given years, were the exports from Company Z more than the average annual exports over the given years?

A.   2
B.   3
C.   4
D.  5
Answer : Option C

Explanation:

Average annual exports of Company Z during the given period
  = \frac{1}{7} \times \!(60 +90 +120 + 90 +60 + 80 + 100)
= Rs  [   ( \frac{600}7}  ) ]crores
= Rs. 85.71 crores.

From the analysis of graph the exports of Company Z are more than the average annual exports of Company Z (i.e., Rs. 85.71 crores) during the years 1994, 1995, 1996 and 1999,

Multi Graph

A multigraph with multiple edges (red) and several loops (blue). Not all authors allow multigraphs to have loops.

In mathematics, and more specifically in graph theory, a multigraph (in contrast to a simple graph) is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge.

There are two distinct notions of multiple edges:

  • Edges without own identity: The identity of an edge is defined solely by the two nodes it connects. In this case, the term “multiple edges” means that the same edge can occur several times between these two nodes.
  • Edges with own identity: Edges are primitive entities just like nodes. When multiple edges connect two nodes, these are different edges.

A multigraph is different from a hypergraph, which is a graph in which an edge can connect any number of nodes, not just two.

Undirected multigraph (edges without own identity)

A multigraph G is an ordered pair G:=(VE) with

  • V a set of vertices or nodes,
  • E a multi set of unordered pairs of vertices, called edges or lines.

Undirected multigraph (edges with own identity)

A multi graph G is an ordered triple G:=(VEr) with

  • V a set of vertices or nodes,
  • E a set of edges or lines,
  • r : E → {{x,y} : xy ∈ V}, assigning to each edge an unordered pair of endpoint nodes.

Some authors allow multi graphs to have loops, that is, an edge that connects a vertex to itself, while others call these pseudo graphs, reserving the term multi graph for the case with no loops.

Directed multi graph (edges without own identity)

A multi digraph is a directed graph which is permitted to have multiple arcs, i.e., arcs with the same source and target nodes. A multi digraph G is an ordered pair G:=(V,A) with

  • V a set of vertices or nodes,
  • A a multi set of ordered pairs of vertices called directed edgesarcs or arrows.

A mixed multi graph G: = (V,EA) may be defined in the same way as a mixed graph.

Directed multi graph (edges with own identity)

A multi digraph or quiver G is an ordered 4-tuple G:=(VAst) with

  • V a set of vertices or nodes,
  • A a set of edges or lines,

, assigning to each edge its source node,

, assigning to each edge its target node.

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