Data Interpretation

2. Introduction
Data interpretation is a way to organize and present a large
volume of data into a compact and precise form.
Useful tips:
1) Read the question carefully.
2) Analyze the data Carefully.
3) Don’t worry about too much data.
4) Pay close attention to the units used.
5) Learn to Approximate.
6) Learn to skim through data.

3. Approximation:
Approximation is a technique, which is used to find the
solution quickly by rounding off to the nearest integer,
rather than solving for the exact values.

4. Let us understand the concept of this technique better with the help of the following
examples.
Example 1: Find the approximate value of (13.001)3.
a.1900 b.2200 c.2000 d.1800
Solution: 13.001 is approximately equal to 13.
So, instead of finding the cube of 13.001 we can simply find the cube of 13 and tick
the answer nearest to that value.
Now, cube of 13 is 2197 and in options we have 2200, which is nearest to 2197 so the
correct answer is option (b).

5. Example 2: What should replace the question mark in the following equation?
55.003 × 54.998 + 5.003 =?
a.3500 b.3630 c.2540 d.3030
Solution: 55.003 is approximately equal to 55 as well as 54.998 is also approximately
equal to 55.
At the same time, 5.003 is close to 5.
So, the equation reduces to the form 55 × 55 + 5 = 3025 + 5 = 3030.

6. Approximation should be used when the
options in the question are NOT close
enough.

7. Average:
Average is basically the Arithmetic mean of given items.
Mathematically,
Arithmetic Mean = average = Sum of terms/ No. of terms.

8. Example 1: Find the arithmetic mean of first five prime numbers.
Solution: First five prime numbers are 2, 3, 5, 7 and 11. The mean or the
average formula is = Sum/no. = (2 + 3 + 5 + 7 +11)/5 = 5.6.

9. Example 2: Find the average of 56, 41, 59, 52, 42 and 44.
Solution: If the given items are very close to each other, a shortcut may
be used instead of applying the average formula. Assume that the
average is 50, as the terms are around 50 only. Now calculating the
difference of all items with 50, you are getting + 6, - 9, +9, + 2, - 8, -
6. Now, if you add these numbers, the result comes out to be - 6.
That implies this - 6 will be equally distributed among all the terms
and every term will be reduced by - 6/6 = - 1 i.e. average will be
reduced by 1. Thus the real average will be 50 - 1 = 49.

10. Q.1: The average age of M boys is ‘b’ years and of ‘n’ girls ‘c’ years. The
average age of all together is?
A. (mb – nc)/ (m + n) years
B. (mb + nc)/ (m - n) years
C. (mb + nc)/ (m + n) years
D. (mb – nc)/ (m - n) years

11. What is the average amount of interest per year which the company had to pay
during this period?
A.Rs. 32.43 lakhs B.Rs. 33.72 lakhs C.Rs. 34.18 lakhs D.Rs. 36.66
lakhs

12. Ratio:
The ratio of two quantities a and b in the same units, is the
fraction and we write it as a : b.
In the ratio a : b, we call a as the first term or antecedent and b, the
second term or consequent.
For example : The ratio 5 : 9 represents 5/9 with antecedent = 5, consequent =
9.

13. What is the ratio between male employees in Administration and
Printing Departments respectively?
A. 7 : 4 B. 4 : 7 C. 3 : 4 D. 7 : 3

14. Types:-
1. Bar graphs
2. Stacks graphs
3. Tabular
4. Line graphs
5. Pie charts

15. YOU MUST KNOW
Table of Common
Fractions and Their
Percentage Equivalents

17. BAR GRAPHS:-
 Given quantities can be compared by the height or length of
a bar-graph.
 A bar-graph can have either vertical or horizontal bars.
 One can compare different quantities or the same quantity
at different times.
 In bar graph the data is discrete.
 Presentation of data in this form makes evaluation of
parameters comparatively very easy.

18. Example 1.
1. In which of the following year the gap between the import and export of cotton was
maximum?
(1) 2001-2002 (2) 2002-2003 (3) 2003-2004 (4) 2004-2005

19. 2. In which of the following year the gap between the imports and exports was minimum?
(1) 2002 – 2003(2) 2003 – 2004(3) 2004 – 2005(4) None of these
3. The exports in 2001 - 2002 was approximately how many times that of the year 2003-
2004?
(1) 2 (2) 3 (3) 4 (4) 5
4. Give the ratio between the number of years in which export is greater than imports and import
is greater than exports?
(1) 3 : 2 (2) 2 : 3 (3) 3 : 1 (4) 1 : 3
5. Give the difference between the average of imports and exports of cotton over the years?
(1) 100 (2) 90 (3) 80 (4) 70

20. STACK GRAPH

21. Question 1: If the total no. of Apple IOS users in 2010 were 50000,
then what was the number of Android users in the same year?
(1) 2857 (2) 43557 (3) 42857 (4) 52857
Question 3: What was the ratio of the RIM users in 2010 to the Apple
IOS users in 2013?
Question 2: What was the percentage of the Apple IOS users in 2013?
(1) 28% (2) 43% (3) 32% (4) 52%
(1) 15/16 (2) 12/15 (3) 1/15 (4) 5/17

22. TABULAR GRAPH
Example 1– The following table shows the yearly expenditure of a family on different
items from 2009-2013.

23. Question 1 – Find the percentage increase in total expenditure from
year 2009 to 2013.
(1) 16.36% (2) 13% (3) 10.5% (4) 12.44%
Question 2– Expenditure on food in 2009 is what % of expenditure
on education in 2011?
(1) 48.49% (2) 27.77% (3) 18.5% (4) 42.44%
Question 3 – What percent of the total expenditure in 2013 is spent
on clothing?
(1) 16.36% (2) 6.25% (3) 10.5% (4) 12.44%

24. Example 2–Study the following table carefully and answer these
questions. Number of candidates appeared and qualified in a competitive
examination from different states over the years -

25. Question1. Combining the states P and Q together in 1998, what is the percentage of
the candidates qualified to that of the candidates appeared?
(a) 10.87% (b) 11.49% (c) 12.35% (d) 12.54%
Question2. The percentage of the total number of qualified candidates to the total
number of appeared candidates among all the five states in 1999 is:
(a) 11.49% (b) 11.84% (c) 12.21% (d) 12.57%
Question 3. What is the percentage of candidates qualified from State N for all the
years together over the candidates appeared from State N during all the years together?
(a) 12.36% (b) 12.16% (c) 11.47% (d) 11.15%

26. Question4. What is the average of candidates who appeared from State
Q during the given years?
(a) 8700 (b) 8760 (c) 8810 (d) 8990
Question5. In which of the given years the number of candidates
appeared from State P has maximum percentage of qualified
candidates?
(a) 1997 (b) 1998 (c) 2000 (d) 2001

27. LINE GRAPH:-.
Example 1 Figure below is a single line graph comparing two items; in this instance,
time is not a factor. The graph compares the temperature of New York City on each
of the seven days of week.

28. Question 1 – Find the percentage increase in the temperature from
Monday to Wednesday?
(a) 11.49% (b) 16.28% (c) 12.21% (d) 12.57%
Question 2 – Temperature on Thursday is what % of temp. on
Sunday?
(a) 81.49% (b) 91.94% (c) 72.21% (d) 62.57%
Question 3 – What is the overall percentage rise in temp. from
Monday to Sunday?
(a) 41.19% (b) 21.94% (c) 44.2% (d) 32.57%

29. PIE CHARTS:-
The below chart describes the number of different users in percentage.

30. Question 1: If the total number of users were 150,000, then what is the total number of
users using Firefox browsers?
(a) 87000 (b) 36000 (c) 48810 (d) 28990
Question 2: The most used browser is ahead of the least used by how many users?
(a) 48000 (b) 36000 (c) 48810 (d) 28990
Question 3: What is the angle subtended by the chrome users?
(a) 48.7 (b) 36.6 (c) 75.6 (d) 85.6

31. Example 2: The following Pie-Chart shows the Share of Cars sold by each Automobile
company out of the total cars sold in the year 2012. Total number of cars sold = 100,000
units.

32. Question 1 – What is the total number of cars sold by Maruti Suzuki in the year 2012.
(a) 40000 (b) 36000 (c) 48000 (d) 28000
Question 2 – By how much units does the number of cars sold by Hyundai exceed
that of Honda.
(a) 14,000 (b) 10,000 (c) 10,667 (d) 12,000
Question 3 – What is the percentage of cars sold by Maruti-Suzuki to the total cars
sold.
(a) 10% (b) 20% (c) 25% (d) 40%