Efficient Table Analysis Solution
Owning the Dataset
Let's start by understanding what we're working with in this dataset. We have information about cities around the world, including:
- Geographic location (city and continent)
- Temperature data (both maximum and minimum temperatures in \(°\mathrm{C}\))
- Weather conditions (fine, cloudy, etc.)
A quick scan reveals several useful patterns:
- Temperatures range from below freezing to quite warm (over \(30°\mathrm{C}\))
- Cities are spread across multiple continents (Asia, South America, Oceania, etc.)
- Weather conditions vary, with fine weather appearing multiple times
Key insight: For this type of table, sorting will be our most powerful tool. It instantly reorganizes the data to reveal patterns that would take much longer to find manually.
Analyzing Statement 2
Let's start with Statement 2, as it can be quickly verified using a sorting approach.
Statement 2 Translation:
Original: At least one city reporting fine weather had a maximum temperature less than \(0°\mathrm{C}\).
What we're looking for:
- Cities with fine weather
- Among those cities, at least one with maximum temperature \(< 0°\mathrm{C}\)
In other words: Is there any city that's both fine AND has a maximum temperature below freezing?
The most efficient approach is to sort by maximum temperature first. This immediately shows us the coldest cities at the top.
Looking at our sorted data, we can see that:
- Either there are no cities with maximum temperature below \(0°\mathrm{C}\), or
- None of the cities with maximum temperature below \(0°\mathrm{C}\) have fine weather
This means the statement is No.
Analyzing Statement 3
Statement 3 Translation:
Original: For the Asian cities, the median minimum temperature was \(12°\mathrm{C}\).
What we're looking for:
- All cities in Asia
- The median of their minimum temperatures
- Whether this median equals \(12°\mathrm{C}\)
In other words: If we list all minimum temperatures for Asian cities in order, is the middle value (or average of two middle values) exactly \(12°\mathrm{C}\)?
Let's tackle this methodically:
1. First, let's sort by Continent to group all Asian cities together
2. Then, let's sort by Minimum Temperature (ascending) while keeping only Asian cities in view
After sorting, we see there are 8 Asian cities with the following minimum temperatures:
\(-3°\mathrm{C}, -3°\mathrm{C}, 3°\mathrm{C}, 3°\mathrm{C}, 21°\mathrm{C}, 22°\mathrm{C}, 24°\mathrm{C}, 26°\mathrm{C}\)
Since we have an even number of cities (8), the median is the average of the 4th and 5th values:
Median = \((3°\mathrm{C} + 21°\mathrm{C}) ÷ 2 = 24 ÷ 2 = 12°\mathrm{C}\)
Therefore, this statement is Yes.
Analyzing Statement 1
Statement 1 Translation:
Original: The mean maximum temperature for South America was greater than Oceania.
What we're looking for:
- The average maximum temperature for South American cities
- The average maximum temperature for Oceanian cities
- Whether South America's average is higher
In other words: If we calculate the mean maximum temperature for each continent, is South America's mean greater than Oceania's?
Let's approach this efficiently:
1. Sort by Continent to group regions together
2. Look at the maximum temperatures for cities in each region:
- South America: \(29°\mathrm{C}, 38°\mathrm{C}, 29°\mathrm{C}\) (3 cities)
- Oceania: \(25°\mathrm{C}, 29°\mathrm{C}\) (2 cities)
We could calculate the exact means:
- South America: \((29 + 38 + 29) ÷ 3 = 96 ÷ 3 = 32°\mathrm{C}\)
- Oceania: \((25 + 29) ÷ 2 = 54 ÷ 2 = 27°\mathrm{C}\)
Therefore, this statement is Yes.
Final Answer Compilation
Let's combine our findings for each statement:
- Statement 1: Yes
- Statement 2: No
- Statement 3: Yes
Our answer is therefore: Yes, No, Yes
