Data Interpretation Questions and Answers

Answer: B

The approximate average supply in the key is 5375 kg.

With capacity fixed at 10000 kg, each year's supply is capacity times the demand share times the supply share.

\[ \begin{aligned} 2003 &: 10000 \times 0.80 \times 0.65 = 5200 \\ 2004 &: 10000 \times 0.90 \times 0.70 = 6300 \\ 2005 &: 10000 \times 0.80 \times 0.60 = 4800 \\ 2006 &: 10000 \times 0.65 \times 0.90 = 5850 \end{aligned} \]

\[ \text{average} = \frac{22150}{4} = 5537.5 \]

The exact average, 5537.5 kg, is not among the options. The question asks for an approximate value, and 5375 is the closest option to it (about 160 kg away), so the key takes 5375. 6200 is more than 650 kg away, and 5100 and 4400 are further still.

Answer: C

The capacity is highest in 2005.

Supply = capacity × (demand share) × (supply share). If supply is the same every year, capacity is largest where the product of the two shares is smallest.

\[ \begin{aligned} 2003 &: 0.80 \times 0.65 = 0.520 \\ 2004 &: 0.90 \times 0.70 = 0.630 \\ 2005 &: 0.80 \times 0.60 = 0.480 \\ 2006 &: 0.65 \times 0.90 = 0.585 \end{aligned} \]

2005 has the smallest product, 0.48, so the same supply needs the largest capacity behind it. 2004 is the opposite case, with the smallest capacity. 2006 is the trap: its supply share is the highest of all, but its low demand share pulls the product up to 0.585.

Answer: C

Actual profit exceeds estimated profit in 2 years.

\[ \begin{aligned} \text{Est.} &: 295,\ 401,\ 204 \\ \text{Actual} &: 338,\ 210,\ 384 \end{aligned} \]

Each figure is revenue minus cost for 2007, 2008 and 2009. For example, the 2007 estimate is \(1281 - 986 = 295\) and the 2007 actual is \(1326 - 988 = 338\).

Actual profit is higher in 2007 (338 against 295) and in 2009 (384 against 204), but lower in 2008 (210 against 401), because actual sales in 2008 fell short of the estimate while costs ran over. So the count is two, not one or three.

Answer: C

The best forecasting year is 2009.

The measure is estimated sales divided by actual sales, and the question defines the lower value as the better forecast.

\[ \begin{aligned} 2007 &: 1281 \div 1326 \approx 0.966 \\ 2008 &: 1452 \div 1286 \approx 1.129 \\ 2009 &: 1228 \div 1452 \approx 0.846 \end{aligned} \]

2009 gives the lowest ratio, 0.846. 2008 is the worst by this rule, since the estimate exceeded actual sales. 2007 has the ratio closest to 1, which would be the most accurate forecast in ordinary terms, but the question's own rule says lower is better, so the data are enough and 'Cannot be determined' is wrong.

Answer: C

The maximum possible profit is 428.

For each year, take the larger of the estimated and actual revenue and subtract the smaller of the estimated and actual cost.

\[ \begin{aligned} 2007 &: 1326 - 986 = 340 \\ 2008 &: 1452 - 1051 = 401 \\ 2009 &: 1452 - 1024 = 428 \end{aligned} \]

The largest of the three is 428, in 2009, where the actual revenue (1452) was the higher figure and the estimated cost (1024) the lower. 340 and 401 are the values for 2007 and 2008, which catch anyone who stops at the first or second year.

Answer: C

About 38800 asylum seekers applied to countries outside the table.

In 2010 the USA's 72800 applications were 15% of all applications, which gives the total.

\[ \begin{aligned} \text{total} &= \frac{72800}{0.15} \approx 485333 \\ \text{table, 2010} &= 92\% \\ \text{others} &= 8\% \times 485333 \approx 38827 \end{aligned} \]

The 92% is the sum of the fifteen countries' 2010 column (15 + 13 + 11 + 3 + 9 + 6 + 6 + 6 + 4 + 3 + 3 + 4 + 3 + 3 + 3). The remaining 8% is about 38827, which rounds to 38800. 36400 would be 7.5% of the total, and 37800 and 40200 match no share that the table supports.

Answer: C

The number of students fell in Agriculture.

The bar chart gives about 35000 students in 2001 and 40000 in 2002. Multiply each year's total by the faculty's share.

\[ \begin{aligned} \text{Agri. 2001} &= 8\% \times 35000 = 2800 \\ \text{Agri. 2002} &= 5\% \times 40000 = 2000 \end{aligned} \]

Agriculture fell by 800 students. The other two named faculties grew: Commerce went from \(24\% \times 35000 = 8400\) to \(24\% \times 40000 = 9600\), and Pharmacy from 2450 to 3600. 'None' is wrong because a falling share can mean a falling number even when the total rises, as it does for Agriculture.

Answer: B

Item A accounts for 50/3 % of the expenditure, that is \(16\tfrac{2}{3}\)%.

The angles in a pie chart add to 360°.

\[ \begin{aligned} A &= 360 - (65 + 45 + 90 + 100) = 60^\circ \\ \frac{60}{360} \times 100 &= \frac{50}{3}\% \end{aligned} \]

25 is what you get by dividing 60 by 240 instead of 360, and 175/6 and 25/18 do not correspond to 60° of a 360° circle. A sixth of the circle is always \(16\tfrac{2}{3}\)%, a value worth remembering.

Answer: B

Only two pairs are correctly matched.

Convert each angle to a share of 360°.

\[ \begin{aligned} \text{Food} &= \tfrac{108}{360} \times 100 = 30\% \\ \text{Education} &= \tfrac{54}{360} \times 100 = 15\% \end{aligned} \]

Pair 1 (30%) is right. Pair 2 is right: 108 : 54 = 2 : 1. Pair 3 is wrong: the remaining sectors are \(100 - 30 - 15 = 55\%\), not 60%. 60% would need Education to be 10%, that is 36°, not 54°.

Answer: A

The information is correct in only one row.

Reading the bars: Withdrew 8, F 4, D 8, C 6, B 19 and A 3.

• Row 1 gives grade A as 4; the bar is 3 (4 is the F bar). Wrong.
• Row 2: withdrew 8, grade D 8, grade A 3. All correct.
• Row 3 gives grade C as 8; the bar is 6. Wrong.

So only row 2 is fully correct. Each wrong row changes one value, which is why every entry, not just the first, has to be checked.