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The table shows, for each of 10 Irish weather stations and each of 8 calendar months, the average (arithmetic mean) number of days per month that the station recorded snowfall during the years 1961–2000. For example, during this time period, the station at Birr recorded snowfall on an average of 4.5 days in January.
| Station | Jan | Feb | Mar | Apr | May | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|
| Belmullet | 4.6 | 4.3 | 3.5 | 1.7 | 0.2 | 0.0 | 0.7 | 2.7 |
| Birr | 4.5 | 3.3 | 2.5 | 1.0 | 0.2 | 0.0 | 0.5 | 2.5 |
| Claremorris | 6.5 | 5.3 | 4.5 | 1.9 | 0.2 | 0.1 | 1.6 | 3.6 |
| Clones | 6.2 | 5.8 | 4.4 | 1.8 | 0.4 | 0.1 | 1.6 | 3.8 |
| Cork | 3.9 | 4.1 | 2.6 | 1.1 | 0.1 | 0.0 | 0.5 | 2.4 |
| Dublin | 5.6 | 5.0 | 3.8 | 1.6 | 0.3 | 0.1 | 0.9 | 3.0 |
| Kilkenny | 4.5 | 4.3 | 2.7 | 0.9 | 0.1 | 0.0 | 0.5 | 2.4 |
| Mullingar | 6.0 | 5.3 | 3.9 | 2.0 | 0.2 | 0.0 | 1.0 | 3.5 |
| Rosslare | 2.3 | 3.1 | 1.6 | 0.7 | 0.1 | 0.0 | 0.2 | 1.1 |
| Valentina | 1.3 | 1.4 | 1.0 | 0.4 | 0.1 | 0.0 | 0.1 | 0.8 |
For each of the following statements about the weather stations listed in the table, select Must be true if that statement must be true if the information provided is correct. Otherwise, select Might not be true.
The station with the greatest average number of days of recorded snowfall during January of years 1961 through 2000 had the greatest total number of days with recorded snowfall during those years.
Cork had at least 2 days with recorded snowfall during February in each of the years from 1961 through 2000.
In at least one year from 1961 through 2000, the station at Valentia recorded 2 or more days of snowfall in a single calendar month.
Let's take a strategic approach to understanding this table of average snowfall days in Ireland. The data shows the average number of days with snowfall across multiple weather stations over a 40-year period.
Looking at the table, we immediately notice:
Key insights that will help us solve efficiently:
These observations will be crucial for evaluating the statements without unnecessary calculations.
Original: "The station with the greatest average number of days with snow in January is the same as the station with the greatest average total number of days with snow in a year."
What we're looking for:
In other words: Does the station with most January snow days also have the most total snow days?
Let's approach this efficiently. Instead of checking every station, we can directly identify:
Since these are different stations (Claremorris ≠Clones), the statement is MIGHT NOT BE TRUE.
Teaching note: Notice how we avoided calculating 40-year totals entirely. We only needed to identify which stations had the highest values in each category and check if they matched.
Original: "The Valentia station had at least 2 days with snow in at least one month."
What we're looking for:
In other words: Can we determine if Valentia had 2+ snow days in at least one month during those 40 years?
This is where understanding averages becomes crucial. Looking at Valentia's data, we see its highest monthly average is 1.4 days (February).
Let's think about what this average means:
Mathematically, it's impossible to have an average of 1.4 unless some years had 2 or more days. Therefore, Valentia must have had at least one month with 2 or more snow days.
The statement is MUST BE TRUE.
Teaching note: This demonstrates the mathematical necessity principle. When an average exceeds a whole number over many instances, at least some instances must exceed that whole number.
Original: "Cork had at least 2 days with snow every February."
What we're looking for:
In other words: Does Cork's February average of 4.1 days guarantee a minimum of 2 days every year?
This requires understanding a fundamental principle about averages: they tell us nothing definitive about minimums unless we have additional constraints.
For Cork's February average of 4.1 days:
Without additional information about the distribution, we cannot guarantee a minimum of 2 days every February. The statement is MIGHT NOT BE TRUE.
Teaching note: This illustrates the critical "Average Principle" - averages never guarantee minimums without additional constraints.
After analyzing all three statements:
Therefore, the correct answer is: Statement 3 ONLY MUST BE TRUE.
This problem demonstrates how understanding statistical principles can dramatically simplify data analysis questions, allowing us to focus on logical reasoning rather than extensive calculations.
The station with the greatest average number of days of recorded snowfall during January of years 1961 through 2000 had the greatest total number of days with recorded snowfall during those years.
Cork had at least 2 days with recorded snowfall during February in each of the years from 1961 through 2000.
In at least one year from 1961 through 2000, the station at Valentia recorded 2 or more days of snowfall in a single calendar month.