Data Interpretation – Basic Concepts of Qualitative and Quantitative DI Methods (Aptitude, Examples, Answer, Explanation)

Data Interpretation (Basics, Questions and Solved Examples)

What is Data Interpretation?

Data Interpretation is the process of making sense out of a collection of data that has been processed. This collection may be present in various forms like bar graphs, line charts and tabular forms and other similar forms and hence needs an interpretation of some kind. It means understanding, organizing, reviewing and interpreting given data, as to get meaningful conclusions. The data can be provided in various forms like in table format, pie chart, line graph, bar graph, or a combination of these.

What is Data Interpretation Method?

Data interpretation method is a way to analyze and help people make sense of numerical data which has been collected, analyzed and presented. When data is collected, it normally stays in a raw form which may be difficult for the normal person to comprehend and that is why analysts always try to break down the information gathered so that others can make sense of it.

For instance, when Founders present their pitches to his or her potential investors, they do that by interpreting the data such as market size, growth rate and so on for better understanding. There are 2 principal methods by which data interpretation can be done:
  1. Qualitative Methods
  2. Quantitative Methods

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Qualitative Data Interpretation Method

Qualitative data interpretation method is used to analyze qualitative data which is often termed as categorical data. This approach uses texts, rather than numbers or patterns to represent data. Qualitative data requires first to be coded into numbers before it can be analyzed. As the texts are usually cumbersome and take more time. Coding done by the analyst is also documented so that it can be reused by others and also examined further.

There are 2 main types of qualitative data, such as nominal and ordinal data. These two data types are both performed using the same method, but ordinal data interpretation is easier than that of nominal data.

In most of the cases, ordinal data is usually labeled with numbers throughout the process of data collection and so many times coding may not be required. This is different from nominal data which still requires to be coded for proper interpretation.

Quantitative Data Interpretation Method

Quantitative data interpretation method is used to analyze quantitative data which is also termed as numerical data. This data type includes numbers and is therefore can be analyzed with the help of numbers and not texts. It can be further categorized into two main types, such as discrete and continuous data. Continuous data is further divided into interval data and ratio data, with all the data types being numeric.

Due to its natural existence as a number, analysts do not need to use the coding method on quantitative data before analyzing it. The process of analyzing quantitative data requires statistical modeling techniques namely standard deviation, mean and median.



Practice Questions : For Data Interpretation

Example 1 - Directions (1-5): Study the following graph carefully and answer the following questions given below.



Question 1: What is the difference between Number of Girls in School A and Number of Girls in School B?
A) 100
B) 101
C) 102
D) 103
E) None of the above

Answer: Option C
Explanation: School A: B+G = 10035
B-G = 373
Girls = 4831
In School B: B+G = 10098
B-G = 640
G = 4729
Difference = 102

Question 2: Girls in School C forms approximately what percent of the total number students in that School?
A) 45.5%
B) 47.5%
C) 48.5%
D) 49.5%
E) 50%

Answer: Option C
Explanation: B+G = 10087
B-G = 285
G = 4901
% = 4901/10087 = 48.58%

Question 3: What is the ratio of Sum of Boys in School D and Girls in School E together to the Sum of Girls in School D and Boys in School E together is?
A) 997:1012
B) 999:1012
C) 1000:1011
D) 1000:1013
E) None of the above

Answer: Option A
Explanation: School D: B+G = 10081
B-G = 475
B = 5278 G = 4803
In School E: B+G = 10009
B-G = 625
B = 5317 G = 4692
Ratio = (5278+4692):(4803+5317)
9970:10120
997:1012

Question 4: How many number of Boys are there in School F?
A) 5134
B) 5234
C) 5334
D) 5444
E) None of the above

Answer: Option B
Explanation: B+G = 10045
B-G = 423
Boys = 5234

Question 5: In which of the following School least no of Girls are present?
A) School A
B) School B
C) School C
D) School D
E) School E

Answer: Option E
Explanation: From above calculations:
School A: 4831
School B: 4729
School C: 4901
School D: 4803
School E: 4692



Example 2 - Directions (6-10): Study the Pie Chart and answer the following questions.


Note: Cakes sold everyday = No. of Vanilla Cakes + No. of Chocolate Cakes

Question 6: The ratio of Number of Vanilla Cakes Sold to Chocolate Cakes Sold is 2:1 of the total cakes sold on Monday and the ratio of the number of Vanilla Cakes Sold to Chocolate Cakes Sold is 3:2 in the total Cakes sold on Wednesday. Then difference of Vanilla Cakes Sold on Monday and Vanilla Cakes sold on Wednesday is?
A) 13
B) 14
C) 15
D) 16
E) None of the above

Answer: Option B
Explanation: Monday Cakes sold = 84*11.5 = 966
Ratio of Vanilla: Chocolate = 2:1
Vanilla = 644
Wednesday: 1050
Ratio of Vanilla: Chocolate = 3:2
Vanilla = 630

Question 7: If the ratio of Vanilla Cakes Sold on Thursday to Vanilla Cakes sold on Saturday is 3:4, Number of Chocolate Cakes Sold on Thursday is equal to Number of Chocolate on Saturday then Number of Chocolate Cakes sold on Saturday is equal to total number of Cakes sold on which day?
A) Monday
B) Tuesday
C) Wednesday
D) Thursday
E) Friday

Answer: Option A
Explanation: Thursday = V1+C = 1218
Saturday = V2+ C = 1302
V2-V1 = 84
V1:V2 = 3:4
V1 = 252 V2 = 336
Then, C = 996 = 84*11.5 =i.e., Total Cakes sold on Monday.

Question 8: If the average number of Vanilla Cakes Sold on Friday and Sunday are 858 and Number of Chocolate Cakes Sold on Sunday are 72 more than Number of Chocolate Cakes sold on Friday then Number of Chocolate Cakes sold on Friday is?
A) 482
B) 492
C) 498
D) 512
E) None of the above

Answer: Option B
Explanation: Friday = 1344 = V1+C1
Sunday = 1428 = V2+C2
Average = (V1+V2)/2 = 858 then V1+V2 = 1716
2772 = 1716+C1+C2
C1+C2 = 1056
C2-C1 = 72
C1 = 492 = Friday Chocolate Cakes

Question 9: Ratio of Vanilla Cakes Sold to Chocolate Cakes Sold is 46:45 on Tuesday then how many number of Vanilla Cakes are Sold on that day?
A) 540
B) 546
C) 552
D) 562
E) None of the above

Answer: Option C
Explanation: Cakes = 84*13 = 1092
Vanilla = 1092*46/91 = 552

Question 10: If the ratio of Vanilla Cakes sold to Chocolate Cakes sold on Monday is 2:1 and the ratio of Selling Price of Vanilla Cake to Chocolate Cake is the 1:4, total amount earned by him on Monday is Rs.9660 then what is the rate of One Vanilla Cake?
A) Rs 4
B) Rs 5
C) Rs 10
D) Rs 20
E) None of the above

Answer: Option B
Explanation: Vanilla = 966*2/3 = 644
Chocolate = 966*1/3 = 322
R1:R2 = 1:4
644R1+322R2 = 9660
R1 = 5

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Example 3 - Directions (11-16): Study the following graph carefully and answer the following questions given below.




Question 11: The Amount invested by Vikram in savings scheme G is equal to the amount invested by him in savings scheme B. The rate of interest (p.c.p.a.) of savings scheme G and B are the same. The only difference is that savings scheme G offers compound interest (compounded annually) whereas the savings scheme B offers simple interest. If the difference between the interest earned by Vikram from both the schemes after 2 years is Rs. 349.92, what is the rate of interest?
A) 6%
B) 5%
C) 3%
D) 4%
E) 9%

Answer: Option E
Explanation:

Savings Scheme Vikram and Deepa’s Investment Vikram’s Investment Deepa’s Investment
A 84000 43680 40320
B 72000 43200 28800
C 32000 12800 19200
D 60000 18000 42000
E 64000 25600 38400
F 96000 61440 34560
D = PR²/(100)2
R² = D×(100)2/P
R = √D×(100)2/P = √349.92×100×100/43200
R = 9%

Question 12: Deepa invested in savings scheme F for 4 years. If the savings scheme F offers simple interest at the rate of 7 p.c.p.a. for the first two years and then compound interest at the rate of 10 p.c.p.a. (compounded annually) for the third and fourth year, what will be the interest earned by Deepa after 4 years?
A) 12,364
B) 12,096
C) 12,242
D) 12,542
E) 12,112

Answer: Option B
Explanation: The interest earned by Deepa after 4 years = 34560×7×2/100 + 34560 (1+10/100)²-34560
= 34560×7×2/100+34560(121-100/100)
= 34560/100(14+21)
= 12096/-

Question 13: What is the respective ratio between the total amount invested by Vikram in scheme C and E together and the total amount invested by Deepa in the same savings scheme together?
A) 3:2
B) 3:4
C) 1:4
D) 2:3
E) 3:1

Answer: Option D
Explanation: Required Ratio = (12800+2560) : (19200+38400)
= 38400 : 57600
= 2:3

Question 14: Savings Scheme A offers simple interest at a certain rate of interest (p.c.p.a.). If the difference between the interests earned by Vikram and Deepa from Savings Scheme A after 4 years is Rs.4435.50, what is the rate of interest (p.c.p.a)?
A) 15%
B) 23%
C) 33%
D) 24%
E) 25%

Answer: Option C
Explanation: 43680×R×4/100-40320×R×4/100 = 4436.520
13440R = 4436.520×100
R = 443652/13440
= 33%

Question 15: What is the average amount invested by Vikram in savings schemes A, B, C, D and E together?
A) Rs. 29,248/-
B) Rs. 30,562/-
C) Rs. 31,126/-
D) Rs. 29,688/-
E) Rs. 28,656/-

Answer: Option E
Explanation: Required average amount = 43680 + 43200 + 12800 + 18000 + 25600 / 5
= Rs. 28656/-

Question 16: What is the difference between the average amount invested in Savings schemes A, B, D and E by Vikram and the average amount invested in Savings schemes B, C, E and F by Deepa?
A) 2540
B) 2760
C) 2560
D) 2320
E) 2380

Answer: Option E
Explanation: Average amount invested in schemes A, B, D and E by Vikram = (43680 + 43200 + 18000 + 25600)/4 = 90240/4 = 32620
Average amount invested in schemes B, C, E and F by Deepa = (28800 + 19200 + 38400 + 34560)/4 = 119680/4 = 30240
Difference = 32620 – 30240 = 2380



Example 4 - Directions (17-24): Study the following graph carefully to answer the given questions.


Time taken by the pipes to fill a tank/cistern (hours/minutes)

Question 17: A large cistern can be filled by two pipes P and Q. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?
A) 6.5 minutes
B) 7.5 minutes
C) 8.5 minutes
D) 9.5 minutes
E) None of the above

Answer: Option B
Explanation: Part filled by P and Q = 1/15 + 1/10 = 1/6
Part filled by Q = 1/10
x/2(1/6 + 1/10) = 2/15 = 15/2 = 7.5 minutes

Question 18: Two pipes M and N can fill a tank. If both the pipes are opened simultaneously, after how much time should N be closed so that the tank is full in 8 minutes?
A) 14 minutes
B) 12 minutes
C) 15 minutes
D) 18 minutes
E) None of the above

Answer: Option D
Explanation: Required time = y(1-(t/x)) = 27(1-(8/24)) = 18 minutes

Question 19: Three pipe E, F and R can fill a tank. If Pipe R alone can fill a tank in 24 minutes then the pipe R is closed 12 minutes before the tank is filled. Then, in what time the tank is full?
A) 8.(5/13)
B) 8.(4/13)
C) 7.(4/13)
D) 8.(6/13)
E) None of the above

Answer: Option B
Explanation: Let T is the time taken by the pipes to fill the tank
(1/12 + 1/18 + 1/24)*(T – 12) + (1/12 + 1/18)*12 = 1
We will get T = 108/13 = 8.(4/13)

Question 20: Two pipes C and D can fill a cistern. If they are opened on alternate minutes and if pipe C is opened first, in how many minutes will the tank be full?
A) 4 minutes
B) 5 minutes
C) 2 minutes
D) 6 minutes
E) None of the above

Answer: Option D
Explanation: Pipe P can fill = 1/12
Pipe Q can fill = 1/4
For every two minutes, 1/12 + 1/4 = 1/3 Part filled
Total = 6 minutes

Question 21: Two pipes, A and B are opened simultaneously and it is found that due to the leakage in the bottom, 17/7 minutes are taken extra to fill the tank. If the tank is full, in what approximate time would the leak empty it?
A) 27 minutes
B) 32 minutes
C) 36 minutes
D) 39 minutes
E) None of the above

Answer: Option D
Explanation: Total time taken by both pipes before the leak was developed = 60/7 minutes
now, leaks is developed which will take T time to empty the tank so, (1/15 +1/20 – 1/T) = 1/11
solve for T, we will get 660/17 minutes = 39 minutes (approx.)

Question 22: A waste pipe, W can carry off 12 litre of water per minute. If all the pipes I, J and W are opened when the tank is full and it takes one hour to empty the tank. Find the capacity of the tank.
A) 30 ltrs
B) 45 ltrs
C) 60 ltrs
D) 75 ltrs
E) None of the above

Answer: Option C
Explanation: Let the waste pipe take ‘T’ time to empty the tank.
(1/10 + 1/12 – 1/T)*60 = -1
We will get T = 5 min
So capacity = 5*12 = 60 ltrs

Question 23: Two pipes E and F are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When is the cistern full, in what time will the leak empty it?
A) 72 hours
B) 62 hours
C) 64 hours
D) 84 hours
E) None of the above

Answer: Option A
Explanation: Work done by the two pipes in 1 hour = (1/12)+(1/18) = (15/108).
Time taken by these pipes to fill the tank = (108/15)hrs = 7 hours 12 min.
Due to leakage, time taken = 7 hours 12 min + 48 min = 8 hours
Work done by two pipes and leak in 1 hour = 1/8.
Work done by the leak in 1 hour =(15/108)-(1/8)=(1/72).
Leak will empty the full cistern in 72 hours.

Question 24: Three pipes C, A and B can fill a tank. If pipe C is opened all the time and pipe A and B are opened for one hour alternatively. The tank will be full in
A) 5 hrs
B) 6 hrs
C) 7 hrs
D) 8 hrs
E) None of the above

Answer: Option C
Explanation: (1/12 + 1/15) + (1/12 + 1/20) = 17/60 (in 2 hrs this much tank is filled)
so in 6 hrs 51/60 is filled. Remaining, 9/60 = (1/12 + 1/15)*t, so T = 1hr
so total = 6 + 1 = 7 hrs



Example 5 - Directions (25-32): Study the following graph carefully to answer the given questions.



Question 25: P and R started the work jointly. A few days later U also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.600. What is the Share of U?
A) Rs. 360
B) Rs. 385
C) Rs. 240
D) Can’t be determined
E) None of the above

Answer: Option C
Explanation: Efficiency of P = 4%
Efficiency of R = 2%
[(4+2)*10] = 60%
The remaining work was done by U = 40%.
40% of 600 = 240

Question 26: Q and S work together for 5 days, the rest of the work is finished by M in two more days. If they get Rs. 6000 as wages for the whole work, what are the daily wages of Q, S and M respectively?
A) 200, 250, 300
B) 300, 200, 250
C) 600, 400, 200
D) 600, 400, 500
E) None of the above

Answer: Option D
Explanation: Q’s 5 days work = 50%
S’s 5 days work = 33.33%
M’s 2 days work = 16.66% [100- (50+33.33)] Ratio of work of Q, S and M = 3: 2: 1
Q’s total share = Rs. 3000
S’s total share = Rs. 2000
M’s total share = Rs. 1000
Q’s one day’s wage = Rs. 600
S’s one day’s wage = Rs. 400
M’s one day’s wage = Rs. 500

Question 27: The efficiency of L is 25% more than P. L started a work alone and then P joined her 5 days before actual completion of the work. For how many days L worked alone?
A) 9
B) 11
C) 10
D) 25
E) 12

Answer: Option B
Explanation: Efficiency (L : P) = 5 : 4
Number of days(L : P) = 4x : 5x = 4x : 25
∴ Number of days required by L to finish the work alone = 4x
= 4 x 5 = 20.
L and P work together for last 5 days = 5 x 9 = 45%
Efficiency of L = 5% and P’s efficiency = 4%
∴ No. of days taken by L to complete 55% work = 55/5 = 11days

Question 28: R started the work and left after some days, when 25% work was don
E) After it Z joined and completed it working for 25 days. In how many days R and Z can do the complete work, working together?
A) 6
B) 8
C) 10
D) 12
E) 20

Answer: Option E
Explanation: Efficiency of R = (100/50) = 2%
Rest work = 75%
∴ Efficiency of Z = 75/25 = 3%
∴ Combined efficiency of R and Z = 5%
∴ Number of days required by R and Z to work together = 100/5 = 20 days.

Question 29: T and V started the work. After 3 days Z joined them, who can complete alone the same whole work in 3 days. What is the total number of days in which they had completed the work?
A) 12
B) 8
C) 4
D) 6
E) None of the above

Answer: Option C
Explanation: Efficiency of T and V = 11.11 + 5.55 = 16.66%
Work done in 3 days = 3 x 16.66 = 50%
Rest work done by T, V and Z = 50/50 = 1 day
Work can be completed in 4 days.

Question 30: A is twice efficient as B and together they do the same work in as much time as T and V together. In how many days A can complete the work individually?
A) 5 days
B) 8 days
C) 4 days
D) 9 days
E) None of the above

Answer: Option D
Explanation: 1/x + 1/2x = 1/9 + 1/18
3/2x = 3/18
Number of days taken by A = 9 days

Question 31: After working for 3 days S is joined by O. If they complete the remaining work in 3 more days, in how many days can O alone complete the work?
A) 10 days
B) 8 days
C) 5 days
D) 12 days
E) 15 days

Answer: Option C
Explanation: Total days S worked = 3+3 = 6
6/15 = 2/5
So 3/5 = 3/x
x = 5

Question 32: X can do a certain work in the same time in which Y and R together can do it. If X and Y together could do it in the same time as that of Q then Y alone could do it in:
A) 15 days
B) 20 days
C) 25 days
D) 30 days
E) 35 days

Answer: Option C
Explanation: X, Y and R’s 1 day work = 1/10 + 1/50 = 6/50 = 3/25
X’s 1 day work = Y + R‘s 1 day work
2*( x’s 1 day work) = 3/25
x’s 1 day work = 3/50
Y’s 1 day work = 1/10 – 3/50 = 2/50 = 1/25

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