MYP 3 · Maths

INTERPRETING TABLES AND GRAPHS

Interpreting tables

QUESTION 1 [5 marks] — Criterion A Medium
MonthJanFebMarAprMay
Rainfall (mm)85627895110
The table shows monthly rainfall (mm) recorded at a weather station.
MonthJanFebMarAprMay
Rainfall (mm)85627895110
a. State the rainfall in March.
[1]
Show Solution
78 mm
b. Find the total rainfall over the 5 months.
[2]
Show Solution
$$85+62+78+95+110=430 \text{ mm}$$
c. Find the difference between the wettest and driest months shown.
[2]
Show Solution
Wettest: May (110 mm). Driest: Feb (62 mm). Difference $=110-62=48$ mm.
QUESTION 2 [6 marks] — Criterion A Medium
BusCarWalkTotal
Grade 91824850
Grade 101530550
Total335413100
The two-way table shows how students in two grades travel to school.
BusCarWalkTotal
Grade 91824850
Grade 101530550
Total335413100
a. How many Grade 10 students travel by car?
[1]
Show Solution
30 students
b. What percentage of ALL 100 students walk to school?
[2]
Show Solution
$$\frac{13}{100}\times100=13\%$$
c. Which grade has a higher proportion of bus travellers, and by how many percentage points?
[3]
Show Solution
Grade 9: $\frac{18}{50}\times100=36\%$. Grade 10: $\frac{15}{50}\times100=30\%$. Grade 9 is higher, by $36-30=6$ percentage points.
QUESTION 3 [6 marks] — Criterion B Medium
Year20192020202120222023
Sales ($1000s)210195230265310
Investigate the year-on-year percentage change in a company's sales.
Year20192020202120222023
Sales ($1000s)210195230265310
a. Calculate the percentage change in sales from 2019 to 2020, and from 2022 to 2023.
[3]
Show Solution
2019?2020: $\frac{195-210}{210}\times100=-7.14\%$ (a decrease). 2022?2023: $\frac{310-265}{265}\times100=16.98\%$ (an increase).
b. Calculate the percentage change for every other consecutive pair of years, and describe the overall pattern in the company's growth rate.
[3]
Show Solution
2020?2021: $\frac{230-195}{195}\times100=17.9\%$. 2021?2022: $\frac{265-230}{230}\times100=15.2\%$. After the initial dip, the company shows strong, fairly consistent double-digit percentage growth each year from 2020 onward.
QUESTION 4 [4 marks] — Criterion C Medium
BusCarWalkTotal
Grade 91824850
Grade 101530550
Total335413100
A classmate reads the two-way table above (student travel to school) and claims: 'more Grade 10 students walk than Grade 9 students, since walking is listed as only 5 for Grade 10 vs 8 for Grade 9... wait, that's backwards from what I said.'
a. Correct the classmate's confused statement: which grade actually has MORE students walking, using the table?
[1]
Show Solution
Grade 9 has more students walking (8) compared to Grade 10 (5).
b. Explain a reliable strategy for reading a two-way table accurately: how do you find the right row and column intersection for a specific data point (e.g. 'Grade 10 students who walk')?
[3]
Show Solution
Find the row labelled with the category you want (e.g. 'Grade 10'), then move along that row until you reach the column labelled with the second category (e.g. 'Walk') — the value at that exact row-column intersection is the answer. Reading carelessly or mixing up rows and columns is a common source of errors.
QUESTION 5 [5 marks] — Criterion D Medium
ItemRentFoodTransportSavingsOther
Monthly cost ($)950420180250200
A family's monthly budget is shown in the table.
ItemRentFoodTransportSavingsOther
Monthly cost ($)950420180250200
a. Find the family's total monthly spending (all categories combined).
[2]
Show Solution
$$950+420+180+250+200=2000$$
b. The family's monthly income is \$2,200. Are they spending within their means? If they want to increase Savings to \$400 without changing income, which OTHER category(s) would need to be reduced, and by how much in total?
[3]
Show Solution
Yes, they currently spend \$2000 of \$2200 income (\$200 left over). To increase Savings from \$250 to \$400 (a \$150 increase) while keeping total spending at or under \$2200, they could use their current \$200 surplus — no other category needs cutting, since $2000+150=2150 \le 2200$.
QUESTION 6 [6 marks] — Criterion A Medium
CityTokyoLondonCairoNairobiOsloReykjavik
Avg. daily solar hours5.83.49.46.93.93.0
The table shows average daily solar sunshine hours in 6 cities, used for a renewable energy feasibility study.
CityTokyoLondonCairoNairobiOsloReykjavik
Avg. daily solar hours5.83.49.46.93.93.0
a. Which city has the most solar potential, and by how many hours per day does it exceed the LEAST sunny city?
[2]
Show Solution
Cairo (9.4 hours) has the most. Excess over Reykjavik (3.0, the least): $9.4-3.0=6.4$ hours.
b. Find the mean daily sunshine hours across all 6 cities, to 2 decimal places.
[2]
Show Solution
$$\frac{5.8+3.4+9.4+6.9+3.9+3.0}{6}=\frac{32.4}{6}=5.40 \text{ hours}$$
c. A solar company requires AT LEAST 5.5 average daily hours to consider a location commercially viable. List which cities qualify.
[2]
Show Solution
Tokyo (5.8) and Cairo (9.4) and Nairobi (6.9) qualify — the three cities with values above 5.5.
QUESTION 7 [5 marks] — Criterion A Medium
Under 1818-40Over 40Total
Vaccinated4206805101610
Not vaccinated18014070390
Total6008205802000
A public health department's vaccination data for 2,000 residents is shown in the two-way table.
Under 1818-40Over 40Total
Vaccinated4206805101610
Not vaccinated18014070390
Total6008205802000
a. What percentage of the 18-40 age group is vaccinated?
[2]
Show Solution
$$\frac{680}{820}\times100\approx82.9\%$$
b. Which age group has the LOWEST vaccination rate (as a percentage of its own group), and what is that rate?
[3]
Show Solution
Under 18: $\frac{420}{600}\times100=70\%$. 18-40: $\approx82.9\%$ (from part a). Over 40: $\frac{510}{580}\times100\approx87.9\%$. The Under 18 group has the LOWEST rate, at 70%.
QUESTION 8 [4 marks] — Criterion A Hard
Year201820192020202120222023
EV sales (1000s)4568102178295412
The table shows annual electric vehicle (EV) sales (in thousands) in a country over 6 years.
Year201820192020202120222023
EV sales (1000s)4568102178295412
a. Find the year-on-year PERCENTAGE growth for each consecutive pair of years.
[4]
Show Solution
2018?19: $\frac{68-45}{45}\times100\approx51.1\%$. 2019?20: $\frac{102-68}{68}\times100\approx50.0\%$. 2020?21: $\frac{178-102}{102}\times100\approx74.5\%$. 2021?22: $\frac{295-178}{178}\times100\approx65.7\%$. 2022?23: $\frac{412-295}{295}\times100\approx39.7\%$.
QUESTION 9 [6 marks] — Criterion B Hard
Investigate whether the growth PATTERN in EV sales (from the table above) is accelerating, decelerating, or roughly constant, using the percentage growth rates you calculated.
Year201820192020202120222023
EV sales (1000s)4568102178295412
a. List the 5 year-on-year percentage growth rates in order (51.1%, 50.0%, 74.5%, 65.7%, 39.7%), and describe whether they show a clear, consistent trend, or a more complex pattern.
[3]
Show Solution
The rates don't show a simple consistent trend — they rise (51.1%?50.0%?74.5%) then fall (74.5%?65.7%?39.7%), suggesting the growth RATE itself peaked around 2020-2021 and has since been slowing, even though sales in absolute terms are still increasing every year.
b. Based on this pattern, would it be reasonable to assume EV sales will KEEP growing at over 50% per year indefinitely? Justify your answer using the recent trend in the data.
[3]
Show Solution
No — the most RECENT data (2022?2023 growth of only 39.7%, down from a peak of 74.5%) suggests the growth rate is DECELERATING, not sustaining indefinitely. This is a common real-world pattern for emerging technology adoption (rapid initial growth eventually slows as the market matures), so extrapolating the early high growth rates far into the future would likely overestimate future sales.
QUESTION 10 [5 marks] — Criterion C Medium
Investigate what information is LOST when a detailed data table is summarized down to just its mean value, using the vaccination data table from earlier.
a. Calculate the OVERALL vaccination rate across all 2,000 residents (not broken down by age group).
[2]
Show Solution
$$\frac{1610}{2000}\times100=80.5\%$$
b. Compare this single overall figure (80.5%) to the THREE separate age-group rates found earlier (70%, 82.9%, 87.9%). Explain what important information a policy-maker would MISS if they were only given the single 80.5% figure, without the age-group breakdown.
[3]
Show Solution
A policy-maker seeing only 80.5% might assume vaccination coverage is fairly uniform, missing that the UNDER-18 group is significantly BEHIND (70%) compared to older groups (up to 87.9%) — this detail matters because it identifies a SPECIFIC group that may need targeted outreach or a different vaccination strategy, information that's completely hidden by a single averaged summary statistic.
QUESTION 11 [3 marks] — Criterion C Medium
ProductJan SalesFeb SalesMar Sales
Widget A34028355
Widget B210225198
A store manager reviews a sales table and notices something odd about Widget A's February figure.
ProductJan SalesFeb SalesMar Sales
Widget A34028355
Widget B210225198
a. Explain what appears SUSPICIOUS about Widget A's February sales figure (28) compared to its January (340) and March (355) figures, and suggest a likely explanation (e.g. a data entry error) rather than assuming it reflects a genuine, real sales collapse.
[3]
Show Solution
28 is drastically lower than both neighbouring months (340 and 355) — a sudden 92%+ drop followed by an immediate, complete recovery to normal levels the very next month is highly unusual for typical sales patterns. A far more likely explanation is a DATA ENTRY ERROR (e.g. a missing digit — perhaps '280' was mistyped as '28', or a decimal/typo issue), rather than a genuine one-month sales collapse with no lasting cause.
QUESTION 12 [7 marks] — Criterion D Hard
RegionPopulation (millions)Area (km²)
Region A4.2850
Region B2.83200
Region C6.51450
An urban planner compares 3 regions using population and land area data.
RegionPopulation (millions)Area (km²)
Region A4.2850
Region B2.83200
Region C6.51450
a. Calculate the population DENSITY (people per km²) for each region, and identify which region is most densely populated.
[3]
Show Solution
Region A: $\frac{4.2\text{ million}}{850}\approx4941$ people/km². Region B: $\frac{2.8\text{ million}}{3200}=875$ people/km². Region C: $\frac{6.5\text{ million}}{1450}\approx4483$ people/km². Region A is most densely populated.
b. A politician claims Region C 'has the biggest population problem' since it has the most PEOPLE. Evaluate this claim using density rather than raw population, and explain why density might be a more useful metric for planning infrastructure like housing or transport.
[4]
Show Solution
While Region C does have the highest RAW population (6.5 million), Region A actually has the highest DENSITY (?4941 people/km², compared to Region C's ?4483). Density is often more relevant for infrastructure planning because it reflects how CROWDED an area actually is — a region with a large population spread over a huge area may have plenty of room to expand housing/transport, while a smaller-population but highly dense region may face more acute overcrowding pressures per square kilometre, even with fewer total residents.