Data Interpretation Questions and Answers

Answer: B

The number is 264.

Mathematics teachers are 22% of all teachers.

\[ 22\% \text{ of } 1600 = \frac{22}{100} \times 1600 = 352 \]

The male to female ratio is 3 : 1, so males are three of every four mathematics teachers.

\[ \frac{3}{4} \times 352 = 264 \]

There are 264 male mathematics teachers. The option 352 is all the mathematics teachers, 88 is the female share (one quarter of 352) and 176 is half of them.

Answer: C

The maximum increase was in hospital A.

The change in the number of patients each month is new admissions minus discharges. Adding August, September and October:

• A: \((80 - 56) + (64 - 78) + (87 - 69) = 24 - 14 + 18 = 28\)
• B: \(15 + 26 - 15 = 26\)
• C: \(17 - 19 - 3 = -5\)
• D: \(-11 + 14 + 14 = 17\)

Hospital A's net increase of 28 is the largest. B is close at 26, C actually fell, and D rose by 17. November is outside the period asked about.

Answer: C

The angle for Mathematics is 86.4°.

The total of all marks is 72 + 84 + 96 + 80 + 68 = 400. A sector's angle is its share of 360°:

\[ \theta = \frac{96}{400} \times 360^\circ = 86{\cdot}4^\circ \]

75.6° is the angle for Hindi (84 marks), 72° would be 80 marks out of 400, which is Science, and 64.8° is the angle for English (72 marks).

Answer: D

The correct statement is Ten children do not like any fruit given in the table.

Add the children in the table:

\[ 28 + 26 + 44 + 14 + 28 = 140 \]

150 children were asked, so 150 − 140 = 10 children named some other fruit.

The other statements fail on the numbers. Apple (28) and Guava (26) are not equal. Grapes minus Banana is 28 − 14 = 14, not 16. Mangoes and Banana together make 44 + 14 = 58, while twice Guava is 2 × 26 = 52, so that is not 'two times' either.

Answer: B

The difference is 2 hours.

A pie chart for one day represents 24 hours by 360°, so each degree is 24/360 = 1/15 hour. Sleep has 120° and school 90°:

\[ \begin{aligned} &(120^{\circ} - 90^{\circ}) \times \frac{24}{360} \\ &= 30 \times \frac{1}{15} = 2 \end{aligned} \]

Sleep is 8 hours and school 6 hours. Four hours is the time for play or homework (60°), not the difference asked for; 3 hours would need a gap of 45°, and 1½ hours a gap of 22.5°.

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.