Data Interpretation Questions and Answers

Answer: B

The White part is 10.

Red is \( \frac{1}{2} \) of the chart and equals 40, so the whole chart is 80. White is \( \frac{1}{8} \) of the chart:

\[ \text{White} = \frac{1}{8} \times 80 = 10 \]

As a check, Yellow is 20 and Blue is 10, and \( 40 + 20 + 10 + 10 = 80 \). 20 is the Yellow part, 5 would follow from taking 40 as the whole, and 12 has no basis.

Answer: B

It is a pie chart.

A pie chart is a circle divided into sectors, each sector's angle proportional to the part it represents (part/whole × 360°). It therefore shows at a glance how a whole is split into its parts, for example how a family's income is spent.

A bar graph and a pictograph compare separate quantities side by side, and a histogram shows the frequencies of a grouped continuous variable. None of them is designed to show parts of one whole.

Answer: B

The correct option is (a), (b) and (d) are true but (c) is false.

From the table:

• Boys: 5 + 4 + 11 = 20; girls: 7 + 3 + 10 = 20. So (a) is true.
• Black eyes: 11 + 10 = 21 of 40, more than half. So (b) is true.
• Blue eyes: 5 + 7 = 12, an even number. So (c) is false.
• Brown eyes: 4 + 3 = 7, an odd number. So (d) is true.

Option 1 wrongly rejects (d), option 3 wrongly rejects (a) and accepts (c), and option 4 accepts (c) and rejects (d).

Answer: C

The difference is 27.2°.

In a pie chart each value's central angle is its share of 360°. The total number of computers sold is

\[ 500 + 700 + 840 + 750 + 890 + 820 = 4500 \]

March exceeds January by 840 − 500 = 340 computers, so

\[ \begin{aligned} \text{difference} &= \frac{340}{4500} \times 360^\circ \\ &= 27.2^\circ \end{aligned} \]

Each computer is worth 0.08°. 28.8° would need a difference of 360 computers and 28° one of 350, so a slip in the subtraction or the total gives those options.

Answer: D

The correct statement is that the aggregate marks of Maria and Shehnaz are equal.

\[ \begin{aligned} \text{Maria} &= 74 + 88 + 65 + 73 + 90 = 390 \\ \text{Shehnaz} &= 81 + 78 + 77 + 72 + 82 = 390 \end{aligned} \]

The other statements do not match the table. Maria scores more than Shehnaz in Maths, Science and Hindi, three subjects, so 'only two subjects' is wrong. She scores less in Social Science, which is not a language, so 'all subjects except the languages' is wrong, and she scores more in Hindi, which is one. In Maths and Science together Maria has 88 + 90 = 178 against Shehnaz's 78 + 82 = 160, so Shehnaz's aggregate there is not more.

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.

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 \(45 - 25 = 20\).

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.

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.

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.