Question

question #8
the annual rainfall for 30 cities is shown on the histogram below.
note: each class includes the left - most number, but not the right - most number. the right - most number is included in the next class.
which of the following measurements could represent the smallest data point in the data set?
50.5
49.5
21.8
14.9

Explanation:

Step1: Analyze the first class interval

The first class interval is \(15.00 - 22.00\). According to the note, each class includes the left - most number but not the right - most number. So the values in the first class satisfy \(15.00\leq x<22.00\).

Step2: Check each option

• For \(50.5\): It is in a class higher than the first one (since the last class is \(43.00 - 50.00\) and \(50.5>50.00\)).
• For \(49.5\): It is in the \(43.00 - 50.00\) class (\(43.00\leq49.5 < 50.00\)).
• For \(21.8\): It is in the \(15.00 - 22.00\) class (\(15.00\leq21.8<22.00\)).
• For \(14.9\): Since \(14.9<15.00\), it is not in the given data set (because the first class starts at \(15.00\)).

Answer:

\(14.9\) is not in the data set. Among the valid options in the data set range, the smallest value within the first class interval (where the smallest data point of the data set lies) is \(14.9\) is excluded. The next candidate is \(21.8\) which is in the first class \(15.00 - 22.00\). But wait, re - checking:
The first non - empty class is \(15.00 - 22.00\). The note says each class includes the left - most number. So the smallest data point must be \(\geq15.00\). \(14.9<15.00\) is not in the data. \(21.8\) is in the first class. But wait, no:
The first class is \(15.00 - 22.00\) (includes \(15.00\) but not \(22.00\)). The options:

• \(50.5\): wrong class.
• \(49.5\): wrong class.
• \(21.8\): \(15.00\leq21.8 < 22.00\) (in the first non - empty class).
• \(14.9\): \(14.9<15.00\) (not in the data as per class definition).

So the answer is \(14.9\) is incorrect (out of range), and among the in - range options, there is a mistake. Wait, no:
The problem is to find which could represent the smallest data point. The first class is \(15.00 - 22.00\). So the smallest data point is \(\geq15.00\). \(14.9<15.00\) is invalid. \(21.8\) is in the first class. But wait, no:
Wait, the first bar is for \(15.00 - 22.00\). So the data points start from \(15.00\). \(14.9\) is less than \(15.00\), so it cannot be. \(21.8\) is in the first class. But wait, no:
The note says "Each class includes the left - most number, but not the right - most number. The right - most number is included in the next class". So the first class has data \(x\) such that \(15.00\leq x<22.00\). The smallest possible data point is \(15.00\). But among the options:

• \(50.5\): no.
• \(49.5\): no.
• \(21.8\): yes (\(15.00\leq21.8<22.00\)).
• \(14.9\): no (\(14.9<15.00\)).

So the answer is \(14.9\) (but wait, no! Wait the problem is "could represent the smallest data point". If we assume that there might be a data point at the lower - bound of the first class. But \(14.9\) is less than the lower - bound of the first class (\(15.00\)). So the answer is \(14.9\) is wrong. Wait, no! Wait the first class is \(15.00 - 22.00\). So the data set starts at \(15.00\). So \(14.9\) is not in the data. But maybe there is a typo. Wait, re - checking the options:
If we consider the class intervals:
The first class is \(15.00 - 22.00\) (includes \(15.00\)). The second \(22.00 - 29.00\) (includes \(22.00\)), etc.
The smallest data point of the data set (since it's a histogram of 30 cities) must be in the first non - empty class. The first non - empty class is \(15.00 - 22.00\). So the smallest data point \(x\) satisfies \(15.00\leq x<22.00\).

• \(50.5\): \(x = 50.5\) is in \(43.00 - 50.00\) (no, \(50.5>50.00\)).
• \(49.5\): \(43.00\leq49.5<50.00\) (wrong class).
• \(21.8\): \(15.00\leq21.8<22.00\) (correct class).
• \(14.9\): \(14.9<15.00\) (wrong).

But wait, the problem says "could represent the smallest data point". If we assume that the first class is \(15.00 - 22.00\) (the left - most number is included). So the smallest data point is \(15.00\). But among the options, \(14.9\) is less than \(15.00\) (invalid). \(21.8\) is in the first class. But maybe the question has a mistake. Wait, no:
Wait the options:
If we consider that the first class is \(15.00 - 22.00\) (the left - end is included). So the smallest data point is \(\geq15.00\). \(14.9<15.00\) is out. \(21.8\) is in the first class. But wait, another approach:
The histogram's first bar is for \(15.00 - 22.00\). So the data set has values starting from[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]