Let's solve the problem step by step.
### Step 1: Understanding the Data
We have a table of earthquake occurrences in Alaska since 1900, categorized by different magnitudes:
- Magnitude 4 to 5: 90 earthquakes
- Magnitude 5 to 6: 20 earthquakes
- Magnitude 6 to 7: 5 earthquakes
- Magnitude 7 or higher: 1 earthquake
### Step 2: Calculate the Total Number of Earthquakes
First, we need to calculate the total number of earthquakes by summing up the earthquakes in each magnitude category.
[tex]\[ \text{Total Earthquakes} = 90 + 20 + 5 + 1 = 116 \][/tex]
### Step 3: Calculate the Percentage for Each Magnitude Category
Now, we can calculate the percentage that each category represents of the total number of earthquakes.
1. Magnitude 4 to 5:
[tex]\[ \text{Percentage}_{4-5} = \left( \frac{90}{116} \right) \times 100 = 77.59\% \][/tex]
2. Magnitude 5 to 6:
[tex]\[ \text{Percentage}_{5-6} = \left( \frac{20}{116} \right) \times 100 = 17.24\% \][/tex]
3. Magnitude 6 to 7:
[tex]\[ \text{Percentage}_{6-7} = \left( \frac{5}{116} \right) \times 100 = 4.31\% \][/tex]
4. Magnitude 7 or higher:
[tex]\[ \text{Percentage}_{7+} = \left( \frac{1}{116} \right) \times 100 = 0.86\% \][/tex]
### Step 4: Complete the Data Table
\begin{tabular}{|c|c|c|}
\hline Magnitude & Number of Earthquakes & Percentage \\
\hline 4 to 5 & 90 & 77.59\% \\
\hline 5 to 6 & 20 & 17.24\% \\
\hline 6 to 7 & 5 & 4.31\% \\
\hline 7 or higher & 1 & 0.86\% \\
\hline
\end{tabular}
### Step 5: Construct the Pie Graph
To construct the pie graph:
1. Magnitude 4 to 5 (77.59%):
- This is the largest section of the pie.
- Label it as "4 to 5: 77.59%".
2. Magnitude 5 to 6 (17.24%):
- This is the next section of the pie.
- Label it as "5 to 6: 17.24%".
3. Magnitude 6 to 7 (4.31%):
- This is a smaller section.
- Label it as "6 to 7: 4.31%".
4. Magnitude 7 or higher (0.86%):
- This is the smallest section.
- Label it as "7 or higher: 0.86%".
Each percentage corresponds to the proportion of the pie chart, where the entire circle represents 100%. The pie chart will visually show the distribution of earthquake magnitudes.
Note: For your actual pie chart, you will divide the circle into sections according to these percentages, making sure each segment's angle is proportional to the percentage it represents. For example, 77.59% of the circle involves an angle of approximately 279.324 degrees ( [tex]\( 77.59 \times 3.6 \)[/tex] ).
