INTERPRETING TABLES AND GRAPHS

Saturday, with 90 visitors.

$$45+62+38+71+55+90+84=445$$

$$445 \div 7 \approx 63.6 \text{ visitors}$$

Between 2019 and 2020 (from 135 down to 98).

$$\frac{175-120}{120}\times100 \approx 45.8\% \text{ increase}$$

Hour 0-1: $15-10=5$ (thousand). Hour 1-2: $40-15=25$ (thousand).

The steeper section (Hour 1-2) shows a much bigger increase (25,000) than the flatter section (5,000) over the same 1-hour period — a steeper line always means the quantity is changing FASTER (a higher rate of change).

A flat (or nearly flat) section of a graph means the quantity has STOPPED CHANGING (it's constant), not that it's declining or 'getting worse' — 'worse' would require the line to actually go DOWNWARDS, which is different from just being flat.

A downward-sloping section means the quantity is actually DECREASING over time — this is genuinely different from a flat section (no change) and should not be confused with it just because both might look 'less exciting' than a steep rise.

March had the lowest revenue (\$2200). A possible reason could be a seasonal slow period, reduced customer spending after the holidays, or a one-off disruption to business.

First 3 months average: $(2400+2650+2200)/3\approx2416.67$. Last 3 months average: $(2800+3100+2950)/3\approx2950$. Since the second average is notably higher, the business does appear to be trending upward overall, despite the March dip.

Wednesday, 790 kL.

Mean: $\frac{820+865+790+910+875+940+905}{7}=\frac{6105}{7}\approx872.1$kL. Range: $940-790=150$kL.

Between 2020 and 2021, decreasing from 410 to 285 — a decrease of 125 km².

2019: 340km². 2021: 285km² — LOWER than 2019, which superficially supports the policy being effective.

No — the complete picture shows deforestation has actually risen SHARPLY since 2021, reaching its HIGHEST level by 2023 (610km², well above even the pre-policy 2019 level of 340km²). This shows why judging a policy's effectiveness from just 1-2 years of data can be misleading: an initial dip might reflect a temporary effect, random fluctuation, or an unrelated factor, rather than genuine long-term policy success — a full, multi-year trend is needed before drawing reliable conclusions.

First 5 min: $(15-0)\div5=3$ km/min. Last 5 min: $(45-44)\div5=0.2$ km/min.

The runner's speed dramatically decreased (from 3 km/min down to just 0.2 km/min) — confirming the runner slowed down significantly toward the end, likely from fatigue. This is visually shown by the graph becoming progressively FLATTER (less steep) toward the right side — a flatter section always indicates a slower rate of change (speed) than a steeper section.

An isolated spike that breaks sharply from an otherwise smooth trend often signals a MEASUREMENT ERROR, a one-off unusual event, or a data recording mistake — not necessarily a genuinely more 'important' or reliable data point. Reliable data typically fits a coherent pattern with the surrounding context; a lone extreme value that doesn't connect logically to its neighbours deserves careful scrutiny rather than automatic trust, precisely because it stands out as inconsistent with everything around it.

'It goes up and down' is vague and could describe almost ANY non-constant graph — it fails to specify WHEN each change happens, the MAGNITUDE of each rise/fall, or WHICH sections are steeper/flatter than others. Good mathematical communication about a graph's trend should identify specific intervals, quantify approximate values or changes, and describe the overall SHAPE precisely enough that someone could roughly reconstruct the graph from the description alone.

Example: 'Temperature rises steadily from a low in January to a peak around July, then falls at a similar steady rate back down to approximately the same level by December, forming a roughly symmetric seasonal pattern.'

Peak at 2pm, with 124 vehicles/hour.

8am (12 vehicles/hour) and 6pm (52 vehicles/hour) are both relatively LOW-traffic periods compared to the midday peak (89-124 vehicles/hour) — during these quieter times, a simpler, fixed-timing traffic light system would likely be sufficient, since there's less risk of significant congestion, saving the cost/complexity of running an adaptive system when it's not really needed.

$\frac{9800-13200}{13200}\times100\approx-25.8\%$ — a significant decrease. A plausible explanation: 2020 was affected by a major global economic disruption (e.g. a pandemic or recession), which is a well-known real-world factor that caused widespread job losses/hiring freezes across many industries during that period.

Growth 2020?2022: $\frac{18900-9800}{9800}\times100\approx92.9\%$. Limitation: this strong growth could be partly (or largely) due to a NATURAL economic recovery/rebound after the 2020 disruption, rather than being solely caused by the investment program — without a comparison to a SIMILAR region WITHOUT the program (a 'control' comparison), it's difficult to isolate how much of this growth is genuinely attributable to the program itself versus broader economic recovery trends.