Question
lector recorded the amount of rainfall in the desert each month over a period of two years. The lists show the number of inches that fel tach month for year 1 and year 2.
Year 1: 2, 2, 0, 0, 0, 1, 2, 2, 3, 2, 2,2
Year 2: 1, 1, 0, 0, 0, 0, 2, 2, 2, 1, 2, 1
What is the difference between the mean monthly rainfall of the two years?
A. 0.5
B. 1.0
C. 1.5
D. 2.0
E. 2.5
Year 1: 2, 2, 0, 0, 0, 1, 2, 2, 3, 2, 2,2
Year 2: 1, 1, 0, 0, 0, 0, 2, 2, 2, 1, 2, 1
What is the difference between the mean monthly rainfall of the two years?
A. 0.5
B. 1.0
C. 1.5
D. 2.0
E. 2.5
Answers
GPT-4o mini
To find the difference between the mean monthly rainfall of the two years, we first need to calculate the mean for each year.
**For Year 1:**
Rainfall amounts are: 2, 2, 0, 0, 0, 1, 2, 2, 3, 2, 2, 2
1. Sum the rainfall amounts:
\(2 + 2 + 0 + 0 + 0 + 1 + 2 + 2 + 3 + 2 + 2 + 2 = 16\)
2. Calculate the mean:
\(\text{Mean} = \frac{\text{Total Rainfall}}{\text{Number of Months}} = \frac{16}{12} \approx 1.33\)
**For Year 2:**
Rainfall amounts are: 1, 1, 0, 0, 0, 0, 2, 2, 2, 1, 2, 1
1. Sum the rainfall amounts:
\(1 + 1 + 0 + 0 + 0 + 0 + 2 + 2 + 2 + 1 + 2 + 1 = 12\)
2. Calculate the mean:
\(\text{Mean} = \frac{\text{Total Rainfall}}{\text{Number of Months}} = \frac{12}{12} = 1.0\)
**Now, find the difference between the means:**
\[
\text{Difference} = \text{Mean of Year 1} - \text{Mean of Year 2} = 1.33 - 1.0 = 0.33
\]
Thus, the difference does not match any of the provided options. Double-checking the calculations, the mean rainfall for Year 1 is \( \frac{16}{12} \approx 1.33 \) and for Year 2 it's \( 1.0 \).
Let's summarize:
- Mean of Year 1: \( 1.33 \)
- Mean of Year 2: \( 1.0 \)
- Difference: \( 1.33 - 1.0 = 0.33 \)
Since this value is not in the options, we conclude that there might be an oversight in options or distances. However, if we consider just an approximate comparison, the closest round differences could fall under:
A. 0.5
or in a specific context (if approximating to common fractions), **0.5** is the most rational based on mathematical rounding from the nearest options to the calculated mean difference.
**For Year 1:**
Rainfall amounts are: 2, 2, 0, 0, 0, 1, 2, 2, 3, 2, 2, 2
1. Sum the rainfall amounts:
\(2 + 2 + 0 + 0 + 0 + 1 + 2 + 2 + 3 + 2 + 2 + 2 = 16\)
2. Calculate the mean:
\(\text{Mean} = \frac{\text{Total Rainfall}}{\text{Number of Months}} = \frac{16}{12} \approx 1.33\)
**For Year 2:**
Rainfall amounts are: 1, 1, 0, 0, 0, 0, 2, 2, 2, 1, 2, 1
1. Sum the rainfall amounts:
\(1 + 1 + 0 + 0 + 0 + 0 + 2 + 2 + 2 + 1 + 2 + 1 = 12\)
2. Calculate the mean:
\(\text{Mean} = \frac{\text{Total Rainfall}}{\text{Number of Months}} = \frac{12}{12} = 1.0\)
**Now, find the difference between the means:**
\[
\text{Difference} = \text{Mean of Year 1} - \text{Mean of Year 2} = 1.33 - 1.0 = 0.33
\]
Thus, the difference does not match any of the provided options. Double-checking the calculations, the mean rainfall for Year 1 is \( \frac{16}{12} \approx 1.33 \) and for Year 2 it's \( 1.0 \).
Let's summarize:
- Mean of Year 1: \( 1.33 \)
- Mean of Year 2: \( 1.0 \)
- Difference: \( 1.33 - 1.0 = 0.33 \)
Since this value is not in the options, we conclude that there might be an oversight in options or distances. However, if we consider just an approximate comparison, the closest round differences could fall under:
A. 0.5
or in a specific context (if approximating to common fractions), **0.5** is the most rational based on mathematical rounding from the nearest options to the calculated mean difference.