Data Interpretation Types and Techniques

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

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

(a) 3/32 (b) 4/67 (c) 7/11 (d) 5/81

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?

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.

  

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

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.

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 ?

Techniques for Percentage

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

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 ?

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)

	Types of pulses

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

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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