Question

Stephen gathered data about the average rainfall in two cities. He organized his data in the given graph.



A bar graph.Short description, A bar graph.,Long description,
The bar graph is entitled Average Rainfall. It shows the month and how many inches of rain fell for both City A and City B.

Month City A City B
January 3 1.5
February 2.5 2
March 3 2.5
April 4 3
May 4.5 4
June 1 1.5
July 0.5 1
August 1 1.5
September 2 4
October 2.5 3
November 1.5 2.5
December 1.5 2

Question
Click on ,begin emphasis,all,end emphasis, the true statements about the data.

Answer options with 5 options
A.
The range of the data for City B is higher than City A.

B.
The range of the data for City A is higher than City B.

C.
The median of the data for City B is higher than City A.

D.
The range of the data is the same for both City A and City B.

E.
The median of the data is the same for both City A and City B.

Answer 1

To determine which statements are true, let's first calculate the range and median of the rainfall data for both cities.

### Data Summary
**City A (inches of rain):**
January: 3
February: 2.5
March: 3
April: 4
May: 4.5
June: 1
July: 0.5
August: 1
September: 2
October: 2.5
November: 1.5
December: 1.5

**City B (inches of rain):**
January: 1.5
February: 2
March: 2.5
April: 3
May: 4
June: 1.5
July: 1
August: 1.5
September: 4
October: 3
November: 2.5
December: 2

### Calculating Range
The **range** is calculated as the difference between the maximum and minimum values.

- **City A:**
- Maximum: 4.5 (May)
- Minimum: 0.5 (July)
- Range = 4.5 - 0.5 = 4

- **City B:**
- Maximum: 4 (September)
- Minimum: 1 (July)
- Range = 4 - 1 = 3

### Calculating Median
The **median** is the middle value when the data is ordered from least to greatest. If there are an even number of values, it is the average of the two middle values.

- **City A (sorted):**
0.5, 1, 1, 1.5, 2, 2.5, 3, 3, 4, 4.5
- There are 12 values, so the median is the average of the 6th and 7th values:
Median = (2.5 + 3) / 2 = 2.75

- **City B (sorted):**
1, 1, 1.5, 1.5, 2, 2, 2.5, 3, 3, 4
- There are 12 values, so the median is the average of the 6th and 7th values:
Median = (2 + 2.5) / 2 = 2.25

### True Statements Evaluation
Now we can evaluate the statements:

A. **The range of the data for City B is higher than City A.**
- False (3 < 4).

B. **The range of the data for City A is higher than City B.**
- True (4 > 3).

C. **The median of the data for City B is higher than City A.**
- False (2.25 < 2.75).

D. **The range of the data is the same for both City A and City B.**
- False (4 ≠ 3).

E. **The median of the data is the same for both City A and City B.**
- False (2.75 ≠ 2.25).

### Conclusion
The true statement about the data is **B. The range of the data for City A is higher than City B.**