Question

Considering only these 5 bird types, what was the total percentage increase in sightings from 2008 to 2009? (Round your answer to the nearest integer.) A. 7% B. 8% C. 14% D. 18%

Short answer

After plugging in the given data for each bird type and performing the calculations, the total percentage increase in sightings from 2008 to 2009 is approximately \(14\%\), which corresponds to option C.

Step-by-step solution

Identify the change in sightings for each bird type

First, we need to identify the total number of sightings for each bird type in both 2008 and 2009, and then find the change in sightings for each bird type. Let the number of sightings for each bird type in 2008 be \(a_i\) and in 2009 be \(b_i\) where i ranges from 1 to 5. The change in sightings for each bird type can be calculated as follows: Change = \(b_i - a_i\)

Calculate the total number of sightings in 2008 and 2009

Next, we need to find the total number of sightings in 2008 and 2009: Total sightings in 2008 = \(\sum_{i=1}^5 a_i\) Total sightings in 2009 = \(\sum_{i=1}^5 b_i\)

Calculate the total change in sightings from 2008 to 2009

To calculate the total change in bird sightings, we need to sum up the change in sightings for all five bird types: Total change in sightings = \(\sum_{i=1}^5 (b_i - a_i)\)

Calculate the percentage increase

Now, we can find the percentage increase in bird sightings from 2008 to 2009 using the following formula: Percentage increase = \(\frac{\text{Total change in sightings}}{\text{Total sightings in 2008}} * 100\)

Round the answer to the nearest integer

Finally, we need to round off the percentage increase to the nearest integer: Rounded percentage increase = \(round(\text{Percentage increase})\) Now that we have followed these steps, we can plug in the given data for each bird type and perform the calculations to find the total percentage increase in sightings from 2008 to 2009. Based on the result, we can select the correct option among A, B, C, or D.

Key concepts

Percentage Increase Calculations

Understanding how to calculate percentage increase is essential when analyzing data over time, like comparing annual bird sightings. Here's a straightforward approach to finding the percentage increase:

Start by determining the difference in value between two time points. In mathematical terms, if the original value is represented as the variable 'V1' and the newer value as 'V2', the change is calculated by the difference 'V2 - V1'. To convert this change into a percentage, we divide it by the original value 'V1' and then multiply the result by 100. The formula looks like this: \[ \text{Percentage Increase} = \left( \frac{V2 - V1}{V1} \right) \times 100 \% \]

When considering data like bird sightings, this approach enables you to quantify how significantly those sightings have increased over a year. Remember, the result must reflect a true increase for us to talk about a percentage increase. If the result is instead a decrease, the percentage value would be negative.

For GED math preparation and beyond, mastering this calculation is not only about getting the right answer but also understanding trends and changes in datasets.

Bird Sightings Data Analysis

Data analysis for bird sightings involves collecting, organizing, and interpreting information about bird patterns and populations. This could be helpful for researchers, bird watchers, or even for educational purposes. Steps to analyze might include:

• Collection: Gathering data on sighting frequency, location, and bird types over stipulated periods.
• Organization: Sorting the data into relevant categories and time frames.
• Analysis: Using statistics, like percentage increase calculations, to summarize and interpret the data.
• Reporting: Presenting findings in a comprehensible format, which might include charts, graphs, or summary reports.

By analyzing bird sightings data, patterns may emerge, such as migratory behaviors or environmental impacts on bird populations, which can lead to better conservation efforts.

GED Math Preparation

Preparing for the GED (General Educational Development) math test involves mastering various mathematical skills including arithmetic operations, understanding of algebra, data analysis, and problem-solving. A typical GED math study plan should cover:

• Basics of Math: Including addition, subtraction, multiplication, and division.
• Fractions and Decimals: Understanding their operations and conversions.
• Algebra: Solving equations and understanding functions.
• Geometry: Getting conversant with shapes, sizes, and the properties of space.
• Statistics: This includes learning to calculate measures like mean, median, mode, and percentage increase, as shown in bird sightings data analysis.

Practice and familiarization with formulas and procedures are key. Rounding numbers, for example, is a concept that appears across the test and can affect the correctness of an answer if not done properly.

Rounding Numbers

Rounding numbers is a mathematical technique used to simplify figures, making them easier to work with or understand, especially when precision is not crucial. To round a number to the nearest integer, for instance, you look at the digit right after the decimal point:

If that digit is 5 or higher, you increase the integer part by 1. If it's lower than 5, you leave the integer part as it is. This rule assumes a base-10 rounding system, which is most commonly used.

For example: \[ round(3.6) = 4 \] \[ round(2.3) = 2 \]

Properly rounding numbers is especially important in standardized tests like the GED, as incorrect rounding can lead to the wrong answer. It's also relevant in data analysis, such as when simplifying the results of a percentage increase before reporting.