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Data Interpretation Questions and Answers

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11.

The following table shows the number of different fruits kept in a carton :

Type of fruitsMangoesApplesOrangesGuavasPome-granates
Number4456423038

If a pie chart is constructed for the above data, what will be the angle of the sector representing apples ?

Exam Year(s)

CTET - 2024,

Answer: C

The angle for apples is 96°.

The total number of fruits is 44 + 56 + 42 + 30 + 38 = 210. Each sector's angle is its share of 360°:

\[ \frac{56}{210} \times 360^{\circ} = 96^{\circ} \]

79.2° and 100.8° would be the angles for 46.2 and 58.8 fruits, and 72° corresponds to 42 fruits, the oranges, so each of those belongs to a different count or a slip in the total.

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12.

In a certain week, the number of patients in a dental clinic was as follows :

DayNumber of patients
Monday25
Tuesday38
Wednesday45
Thursday18
Friday36
Saturday39

Based on above table, choose the wrong statement :

Exam Year(s)

CTET - 2024,

Answer: D

The wrong statement is total number of patients was 200.

Add the six days:

\[ 25 + 38 + 45 + 18 + 36 + 39 = 201 \]

The other statements are correct: the range is \(45 - 18 = 27\); the number exceeded 30 on four of the six days (Tuesday, Wednesday, Friday, Saturday); and the Monday-Wednesday difference is \(45 - 25 = 20\).

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13.

In a pie chart, the marks obtained by a student in Mathematics, Science, Social Science, Hindi and English are respectively represented by sectors of central angles 90°, 80°, 65°, 75° and 50°. If the total marks obtained by the students were 540, then what is the difference of the marks obtained by him/her in Mathematics and English ?

Exam Year(s)

CTET - 2024,

Answer: A

The difference is 60 marks.

The whole pie of 360° represents 540 marks, so each degree stands for 1.5 marks. Mathematics has 90° and English 50°:

\[ \begin{aligned} \text{Difference} &= (90 - 50) \times \frac{540}{360} \\ &= 40 \times 1.5 = 60 \end{aligned} \]

40 is the difference in degrees, forgetting to convert to marks.

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14.

Study the following graph and answer the question:

Line graph of percent profit earned by company ABC: 45 in 2019, 30 in 2020, 40 in 2021 and 55 in 2022

Profit Percent = \(\frac{Income - Expenditure}{Expenditure} \times 100\)
If the income of the company in 2022 was ₹ 620 crores and the expenditure in 2019 was ₹ 300 crores, then the sum of expenditure in 2022 and the income in 2019 (in ₹ crores) is

Exam Year(s)

DSSSB - 2023,

Answer: D

The sum is 835 crore rupees. The graph gives profit percentages of 45 (2019), 30 (2020), 40 (2021) and 55 (2022). In 2022 the income is 620 with a profit of 55 %, so the expenditure is \[\frac{620}{1.55} = 400\] In 2019 the expenditure is 300 with a profit of 45 %, so the income is \[300 \times 1.45 = 435\] The required sum is 400 + 435 = 835. The option 780 would come from using the wrong year's profit, and 810 and 825 do not follow from these values.

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15.

Study the following pie chart and answer the question:
Distribution (degree wise) of the number of mobile phones sold by a dealer during January to May 2022.

Pie chart with angles: January 82.8 degrees, February 61.2, March 50.4, April 73.8 and May 91.8

Total number of mobile phone sold during these five months = 1800
The dealer earned a profit of ₹ 1200 per mobile phone during January and March. The profit per mobile phone was ₹ 1000 during April and May. What was the difference (in ₹) between the total profit earned by the dealer in January and March and the total profit earned in April and May?

Exam Year(s)

DSSSB - 2023,

Answer: C

The difference is 28800 rupees. The sales in each month follow from the angles of the pie chart, out of 360 degrees and 1800 phones, so each degree stands for 5 phones. January: 82.8 x 5 = 414. March: 50.4 x 5 = 252. April: 73.8 x 5 = 369. May: 91.8 x 5 = 459. January and March: (414 + 252) x 1200 = 666 x 1200 = 799200. April and May: (369 + 459) x 1000 = 828 x 1000 = 828000. The difference is 828000 - 799200 = 28800. February is not used in the question, and options such as 28200 and 28400 do not match this calculation.

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16.

Study the following graph which describes the percentage breakup of the total expenditure of four persons (P, Q, R and S) on three items (A, B and C) and answer the question. Please note that any point shown in the middle is the average of the values below and above (e.g., R).

Triangular graph with items A, B and C on its three sides and four marked points P, Q, R and S

The total expenditure of persons P, R and S on the given three items are ₹ 4000, ₹ 6400 and ₹ 3500, respectively. What is the total expenditure of P on item C, of R on item B and of S on item A?

Exam Year(s)

DSSSB - 2023,

Answer: C

The total is 5150 rupees. Reading the triangular graph, each point shows the share of the three items. P has 25 % on item A, 50 % on item B and 25 % on item C. R has 12.5 % on A, 37.5 % on B and 50 % on C. S has 50 % on A, 37.5 % on B and 12.5 % on C. P on item C: 25 % of 4000 = 1000. R on item B: 37.5 % of 6400 = 2400. S on item A: 50 % of 3500 = 1750. The sum is 1000 + 2400 + 1750 = 5150. The values were read from the grid lines, with R marked as the midpoint of the values below and above it, as the question notes.

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17.

Study the given chart.

Bar chart of Cost for four items: Rice about 1500, Wheat about 1200, Oil about 2000 and Vegetables about 800, on a scale from 0 to 2500

What is total cost of rice?

Exam Year(s)

DSSSB PGT - 2023,

Answer: B

The bar chart gives the cost of four items on a scale from 0 to 2500. The bar for rice rises to the gridline marked 1500, while wheat is at about 1200, oil is at 2000 and vegetables are at about 800. The question asks for the cost of rice, which is read straight from the height of its bar, 1500. The value 1200 is the height of the wheat bar, and 1400 and 1300 are not the height of any bar. The answer is 1500, option B.

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18.

A school has 3 sections, A, B and C, of class VI students. The results of half-yearly and annual examinations are shown in the given table.
Answer the question based on this table.

ResultNumber of students
Section ASection BSection C
Students who failed in both exams142115
Students who failed in the half-yearly but passed in the annual exams12109
Students who passed in the half-yearly but failed in the annual exams81411
Students who passed in both exams525862

How many students are there in class VI in the school?

Exam Year(s)

DSSSB PGT - 2023,

Answer: A

There are 286 students in class VI. Add the students in each row of the table across the three sections. Failed in both: 14 + 21 + 15 = 50. Failed in the half-yearly but passed in the annual: 12 + 10 + 9 = 31. Passed in the half-yearly but failed in the annual: 8 + 14 + 11 = 33. Passed in both: 52 + 58 + 62 = 172. The four groups cover every student exactly once, so the total is 50 + 31 + 33 + 172 = 286. The option 172 is only the number who passed both exams, and 276 and 196 do not match any sum of the groups.

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19.

The following table shows the production of five types of two-wheelers by a company in the years 2017–2020.

Years / Two-wheelers2017201820192020Total
B1102019655
B21414161559
B32116131464
B469102651
B52016191671
Total71757777300

In which year was the total production of two-wheelers of types B2 and B3 taken together equal to the total production of two-wheelers of types B4 and B5 taken together?

Exam Year(s)

DSSSB PGT - 2023,

Answer: C

The year is 2019. For each year the production of types B2 and B3 together is compared with that of B4 and B5 together.

\[ 2017:\ 14+21=35,\ 6+20=26 \]

\[ 2018:\ 14+16=30,\ 9+16=25 \]

\[ 2019:\ 16+13=29,\ 10+19=29 \]

\[ 2020:\ 15+14=29,\ 26+16=42 \]

The two sums are equal only in 2019, where both come to 29. In 2017 and 2018 the B2 and B3 total is larger, and in 2020 the B4 and B5 total is larger.

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20.

Consider the percentage of students of different schools involved in various activities.

School→
Activities↓		SSBSCSDS
Games25302023
Music15252520
Academic30202515
Dance25152230

The activities in descending order of average number of students is:

Exam Year(s)

DSSSB PGT - 2023,

Answer: A

The order is Games, Dance, Academic, Music. Averaging the four schools for each activity:

\[ \text{Games} = \frac{25 + 30 + 20 + 23}{4} = 24.5 \]\[ \text{Dance} = \frac{25 + 15 + 22 + 30}{4} = 23 \]\[ \text{Academic} = \frac{30 + 20 + 25 + 15}{4} = 22.5 \]\[ \text{Music} = \frac{15 + 25 + 25 + 20}{4} = 21.25 \]

Descending, that is Games, Dance, Academic, Music, which is option A and not the orders in B, C and D.

The question asks for the average number of students, which is taken to be the average of the four percentage figures for each activity, because all the schools are compared on the same percentage scale. Dance has a higher average than Academic only because DS has 30 in dance against 15 in academic, which is why Dance sits between Games and Academic.

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