Data Interpretation Questions and Answers

Answer: B

The line chart gives the numbers of calculators sold by the five shops as 20, 50, 75, 125 and 100. Their sum is 20 + 50 + 75 + 125 + 100 = 370, and the average over the five shops is 370 / 5 = 74. So the answer is 74, option (B). The values 76, 72 and 78 would need totals of 380, 360 and 390, which do not match the chart, and the point of 125 for the fourth shop is the highest while 20 for the first is the lowest.

Answer: D

Statement I says A's production in Y1 is 50 percent of B's production in Y2. A produced 300 in Y1 and B produced 600 in Y2, and 300 is 50 percent of 600, so statement I is correct. Statement II says the ratio of B's total in Y4 and Y5 to A's total in Y2 and Y3 is 24 : 23. B produced 800 + 400 = 1200 and A produced 600 + 550 = 1150, and 1200 : 1150 = 24 : 23, so statement II is also correct. The question asks for the statement that is NOT correct, and neither statement is wrong, so the answer is Neither I nor II, option (D).

Answer: C

The value of x is 120, which lies between 115 and 125. The total is 2400 students. From the pie chart, school A has 22 % = 528, B has 16 % = 384, D has 17 % = 408 and E has 25 % = 600.

\[ \text{Girls in A} = \frac{6}{11} \times 528 = 288 \]

\[ \text{Girls in E} = 0.60 \times 600 = 360 \]

So the girls from A and E number 288 + 360 = 648. The students from B and D number 384 + 408 = 792, and two thirds of that is 528.

\[ x = 648 - 528 = 120 \]

The other ranges, 95 to 105, 105 to 115 and 125 to 135, do not contain 120.

Answer: B

The percentage is 12%.

The January sales (blue bars) are shirt 3, trouser 5, coat 7, T-shirt 4 and jacket 6, which total 25 million units. Shirts are 3 of those.

\[ \frac{3}{25}\times100=12\% \]

20%, 17% and 25% would need a different shirt figure or total.

The graph is a three-dimensional bar chart with three rows of bars: blue for January, orange for March and grey for May. Only the blue bars are needed here. The values 3, 5, 7, 4 and 6 add to 25, and the share of shirts is 3 out of 25, which is 12%.

Answer: B

The value of \(x\) lies between 3,800 and 4,200; it is exactly 4,000. Cricket is 22.5% and costs ₹ 18,000, so the total is \(\frac{18000}{0.225} = 80000\). Basketball and Hockey together are \(15\% + 20\% = 35\%\), which is 28,000. Football and Golf together are \(18\% + 12\% = 30\%\), which is 24,000. \[ x = 28000 - 24000 = 4000 \] The difference of 5 percentage points of 80,000 is 4,000, so only the interval 3,800 to 4,200 contains it.

Answer: C

The average production is 25% less than C's 2020 production. State production in 2018: A 450, B 550, C 620, so the average is \[ \frac{450 + 550 + 620}{3} = \frac{1620}{3} = 540 \] State C in 2020 produced 720 lakh tonnes. \[ \begin{aligned} \frac{720 - 540}{720}\times 100 &= \frac{180}{720}\times 100 \\ &= 25\% \end{aligned} \] Dividing the same difference of 180 by 540 instead of 720 would give \(33\frac{1}{3}\)%, which is the wrong base, since the question compares with C's 2020 production; 18% and 20% do not come out of these numbers.

Answer: A

The difference is 0. For CS, the average over the four activities is (20 + 25 + 25 + 22) / 4 = 92 / 4 = 23. For dance, the average over the four schools is (25 + 15 + 22 + 30) / 4 = 92 / 4 = 23. The difference is 23 - 23 = 0.

2, 3 and 5 would result only from misreading a cell in the table.

Answer: C

The person eats 100 g of fat.

The three fats together supply 20% + 20% + 5% = 45% of the 2,000 kcal, and every fat gives 9 kcal per gram:

\[ \begin{aligned} \text{Fat energy} &= 0.45 \times 2000 = 900\ \text{kcal} \\ \text{Fat mass} &= 900 / 9 = 100\ \text{g} \end{aligned} \]

44.4 g is the saturated (or unsaturated) fat alone, \(400/9\). 77.8 g is \(700/9\), which uses the 35% carbohydrate share by mistake. 3,600 multiplies the fat energy by 4 instead of dividing by 9.

Answer: C

There are 11 pixels with \(U \le 4\).

Count row by row the entries that are 4 or less:

• Row 1 (0, 1, 0, 2): all 4
• Row 2 (4, 7, 3, 3): 4, 3, 3, that is 3
• Row 3 (5, 5, 4, 4): the two 4s, that is 2
• Row 4 (6, 7, 3, 2): 3 and 2, that is 2

The total is 4 + 3 + 2 + 2 = 11. Counting only values strictly below 4 drops the three 4s and gives 8, which is the trap in option B. 9 and 3 miss further entries.

Answer: A

She earned ₹ 6,100 per shift on average.

The mean number of patients per shift, weighted by the number of shifts, is

\[ \begin{aligned} \bar{X} &= \frac{5(20) + 6(40) + 7(30) + 8(10)}{100} \\ &= \frac{100 + 240 + 210 + 80}{100} = 6.3 \end{aligned} \]

The earning is linear in X, so the average earning is \(1000(\bar{X} - 0.2) = 1000(6.1) = 6100\) rupees. 6,300 is the mean number of patients times 1000, forgetting to subtract the 0.2 per shift. Because the earning rule is linear, averaging X first and averaging the earnings shift by shift give the same 6,100.