Data Interpretation Types and Techniques

data interpretation

Contents of Chapters

  • Ratio 
  • Percentage
  • Rate
  • Average

Representation of Data

  • Tables
  • Line Graph
  • Bar Graph
  • Pie Charts (or Circle Graphs)
  • Venn Diagram

Techniques for Ratio

Eg 1. 2/1352 is close to the ratio 1/676

data interpretation technique

Eg 2. Find the ratio closest to 14.37/241 ?

(a) 3/32 (b) 4/67 (c) 7/11 (d) 5/81
Sol:
data interpretation technique
1/17 × 4/4 = 4/68 or 4/67 closest.

Eg. 3. Which is the highest ratio among 13/447,45/508,28/583,18/531?

Sol: 
Step 1: Reverse the position of the upper value(numerator) and the lower value(denominator).
Step 2 : Take the closest value
Step 3 : the maximum value is the minimum ratio and minimum value is the maximum ratio.
  data interpretation technique

Eg. 4. Which is the highest ratio among 471/525 , 324/411 , 648/749 ?

Sol:
S1: Approximate the given ratio (if the no. of digits in numerator/denominator is more than 2 )
S2: Multiply the numerator by 10 and get the result fraction
S3: Find only the integer value of the result fraction
S4: If any of the integer value of the result fractions is same then find the next decimal places and so on.
S5: Compare the value of the result fractions. The maximum ratio will have maximum value.
data interpretation technique

Eg 5. Consider , 31/83, 15/46, 22/65, then it is required to find which of the among ratio is less than 1/3 ?

Sol:
data interpretation technique 2

Techniques for Percentage

Case 1. To find by how much per cent X is more or less than Y compared to Y.

data interpretation technique 2
Example: 
Example

If A's income is 20% more than B, then how much % B's income is less than that of A's income ?

Sol:
20/120×100

Case 2. To find the percentage change in any value in year M compared to that value in year K.

data interpretation technique 3
Example

The total population of a village is 5000.The number of males and females increases and consequently the population of the village becomes 5600.Find the percentage change in the population?

Sol:
600/5000×100 = 12%

Case 3. To find the original value if the value after its x% increase or decrease is known

DI
Example

Rakesh's salary is increased by 10% and he get now Rs. 5000. Find his salary before the increase ?

Sol:
1+10/100=110/100
5000/110×100 = 4545.45

Case 4. Two percentage value cannot be compared unless the base values are known.

Example

6% of income of Ram is equal to 18% of income of Shyam 10% of income of Shyam is equals to 30% of income of Mohan. Find the total income of Ram, Shyam and Mohan ?

Sol:
Cannot be determined.

Case 5. Two percentage values can be compared in terms of percentage values ( but not in absolute values) when the base values are same ( although base values are not known ) .

Example

A's height is 40% less than that of B, how much percent B's height is more than that of A ?

Sol:
Let A  = 60  and B = 100
40/60×100 = 662/3%

Case 6. To find the value of a parameter in any year K when the % change in its value over two different periods( any period having the year K) are same.

Example
DI

Techniques for Average

DI

Examples

(1) Find the average annual production increase in product over the period 2000 to 2004 ?

DATA INTERPRETATION
% increase in Production during 2000 - 2004 = 45-25/25×100 = 80%
Average % increase during 2000-04 = 80/5 = 16%

(2) The data of  sale of a Company in the different years of its product type x,y,z are as below :

Year X Y Z Total
2001 8 4 30 42
2002 16 16 18 50
2003 18 32 24 74
2004 14 21 20 55
2005 18 16 28 62

(a) In which of the given years the sale of  product Z was close to its average sale over the years?

Sol:
(30+18+24+20+28) = 120
120/5 = 24
So, the year which is closest to the average is 2003.

(b) In which of the given years the sale of product Z was close to its average sale of all the products in the year ?

Sol:
Year Average Sale Sale of Product Z Difference
2001 42/5 = 8.4 30 Difference with average 30-8.4 = 21.6 is very wide, so calculation not required
2002 50/5 = 10 18 18 - 10 = 8
2003 74/5 = 14.8 24 24-14.8 = 9.2
2004 55/5 = 11 20 20-11 = 9
2005 62/5 = 12.4 28 Difference with average = 28-12.4 = 15.6 is very wide, so calculation not required
 so minimum difference with the year is 2002 ,therefor In 2002, the sale of product Z was closer to the average value of all the products in that year.
(c) Production and Exports of Pulses (In Million kg) has been given below
Year 2000-01 2001-02 2002-03 2003-04 2004-05
Exports 114 115 220 180 310
Production 242 340 640 565 930

Find the average proportion of pulses exported as a fraction of the tea produced in the half decade was (a) 0.11 (b) 0.22 (c) 0.36 (d) 0.41 (e) 0.49

Sol: Here none of the given choices are closer to each other, so mental calculation may work. Just observe that exports are generally 1/3rd of production with one year (1990-91) showing nearly 1/2 of production as exports. Hence the required average will be > 1/3 ( = 0.33). Thus 0.36 looks the closest among the alternatives given.

(d) Sectoral Growth Rate of Major Industry Groups (2015-16) are given as

Sectors Weights 2015-2016
Oil 56.6 6.5
Pulses 24.4 7.5
Books 19 8
Overall 100.00

 Find the overall weighted industrial growth rate in 2015-16 ?

Sol:
Weighted average of X = (w1x1+w2x2+w3x3)/(w1+w2+w3)
Required weighted average growth rate in 2001-02 = (56.6×6.5+24.4×7.5+19×8)/(56.6+24.4+19)
= 702.9/100
= 7.03

Example

Directions(1-5): Study the following table and answer the questions given below in
Production of different types of pulses in a company(figures in thousand)

Year
Types of pulses
A
B
C
D
E
2002
180
60
84
100
76
2003
210
90
32
80
48
2004
135
30
44
95
85
2005
190
85
69
125
115
2006
260
95
120
80
120
2007
240
140
161
90
185

1. In which of the given years was the production of B-type pulses close to its average production over given years?
(a) 2005 (b) 2004 (c) 2003 (d) 2002 (e) None
2. In which year the production of D-type pulses was maximum ?
(a) 2003 (b) 2006 (c) 2005 (d) 2007 (e) 2002
3. What was the approximate percentage of production of A-type pulses in 1995 to its total pulses over the years?
(a) 20 (b) 15 (c) 23 (d) 40 (e) 30
4. In which of the following pairs of years was the total production of E-type pulses two lakhs?
(a) 2003 & 2005 (b) 2005 & 2007 (c) 2004 & 2007 (d) 2002 & 2004 (e) None
5. In which of the given years the total production of all types of scooters was minimum ?
(a) 2004 (b) 2006 (c) 2007 (d) 2005 (e) None

Solution

S-1 (a)
average production of B-type pulses over the years (2002-2007) =(60+90+30+85+95+140)/6
= 83 (in thousand)
S-2 (c)
S-3 (b)
Approximate percentage of production of A-type pulses in 2005 to its total production
= Production in 2005 of A-type/Total production of A-type (2002-07)×100
= 190/(180+210+135+190+260+240)×100
= 190/1215×100
= 15
S-4  (e)
Pairs of years Total production of E-type pulses
2003 & 2005 48 + 115 ≠
2005 & 2007 115 + 185 ≠
2004 & 2007 85 + 185 ≠
2002 & 2004 76 + 84 ≠
Note : 2 lakhs = 200 thousands, so it is better to check in which pairs of years, the total production = 200 thousands for E-type pulses
S-5 (a)

Year Total Production of all types pulses
2002 180 + 60 + 84 + 100 + 76 = 500
2003 210 + 90 + 32 + 80 + 48 = 460
2004 135 + 30 + 44 + 95 + 85 = 389 → Minimum
2005 190 + 85 + 69 + 125 + 115 = 444
2006 260 + 95 + 120 + 80 + 120 = 675
2007 240 + 140 + 161 + 90 + 185 = 816


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