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A questionnaire provides 58 Yes, 42 No, and 20 No-Opinion answers. a. In the construction of a pie chart, how many degrees would be in the section of the pie showing the Yes answers? b. How many degrees would be in the section of the pie showing the No answers? c. Construct a pie chart. d. Construct a bar chart.

Short Answer

Expert verified
a) 174 degrees for 'Yes'. b) 126 degrees for 'No'. c) & d) Constructed based on calculations.

Step by step solution

01

Calculate Total Responses

To determine the number of degrees for each section of the pie chart, we first need to calculate the total number of responses. Given:- Yes: 58- No: 42- No-Opinion: 20Total = Yes + No + No-Opinion\( Total = 58 + 42 + 20 = 120 \)
02

Calculate Degrees for 'Yes' Section

Next, we calculate the degrees that correspond to the 'Yes' responses. A full circle in a pie chart is 360 degrees. Therefore, the formula to find the degrees for the 'Yes' section is:\( \text{Degrees for 'Yes'} = \left(\frac{\text{Yes responses}}{\text{Total responses}}\right) \times 360 \)\( \text{Degrees for 'Yes'} = \left(\frac{58}{120}\right) \times 360 = 174^\circ \)
03

Calculate Degrees for 'No' Section

Similarly, calculate the degrees for the 'No' section. Use the formula:\( \text{Degrees for 'No'} = \left(\frac{\text{No responses}}{\text{Total responses}}\right) \times 360 \)\( \text{Degrees for 'No'} = \left(\frac{42}{120}\right) \times 360 = 126^\circ \)
04

Verify Degrees for 'No-Opinion' Section

To verify our calculations, we calculate the degrees for the 'No-Opinion' responses and check if the total is 360 degrees.\( \text{Degrees for 'No-Opinion'} = \left(\frac{20}{120}\right) \times 360 = 60^\circ \)Verification: \( 174^\circ + 126^\circ + 60^\circ = 360^\circ \)
05

Construct the Pie Chart

Using the degree calculations, construct the pie chart with the sections clearly labeled: - 'Yes' section: 174 degrees - 'No' section: 126 degrees - 'No-Opinion' section: 60 degrees. Ensure the pie chart visually represents each portion of the total responses appropriately based on the degree calculations.
06

Construct the Bar Chart

Create a bar chart representing the data: - Draw three bars labeled 'Yes', 'No', and 'No-opinion'. - The height of each bar corresponds to the number of responses: - 'Yes': 58 - 'No': 42 - 'No-opinion': 20. Ensure the chart is accurate and labeled with units and categories.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Pie Charts
A pie chart is a circular statistical graphic used to represent data sets in a visual and easy-to-understand format. Each "slice" of the pie corresponds to a data category, and the size of each slice is proportional to its contribution to the total data set. Pie charts are excellent for showing proportions and percentages among various categories.

To draw a pie chart, follow these steps:
  • Start by calculating the total number of responses or data points collectively.
  • Next, figure out the percentage each category contributes to the total.
  • Convert these percentages into degrees to allocate the respective sections of the pie chart.
In a full circle, there are 360 degrees. For example, if a category has 50% of the total responses, it will occupy 180 degrees of the pie chart.

However, pie charts have their limitations. They work well with a small number of categories, but as the number of categories increases, the slices can become too small to distinguish, making it less effective. Still, when used correctly, pie charts can quickly showcase how a particular part compares to the whole.
Creating Bar Charts
A bar chart is another popular type of data visualization that uses rectangular bars to represent data values. Each bar's height (or length, in the case of horizontal bar charts) is proportional to the value it represents. Bar charts are great for displaying categorical data and making quick comparisons.

Here's how to make a bar chart:
  • List the categories to be compared, such as 'Yes,' 'No,' and 'No-Opinion.'
  • Draw a bar for each category with a height representing the number of responses collected for that category.
  • Label the bars clearly, including axes indicating categories and response numbers.
Bar charts are particularly useful when you want to display actual values rather than percentages or fractions. They can accommodate many categories and make it easy to compare different groups' sizes.

It’s important to keep your charts simple: when there's too much detail or too many colors, it can become confusing rather than informative. Consistency in color coding and labeling ensures the data is easy to read and interpret.
Key Points of Statistics
Statistics is the science of collecting, analyzing, interpreting, and presenting data. It provides methods for making sense of complex datasets, which is essential for accurate decision-making and predictions.

In practice, statistics involves several important processes:
  • Data Collection: Gathering information from various sources using methods like surveys, experiments, or observations.
  • Data Analysis: Using mathematical and computational techniques to find patterns or trends. This includes calculations such as mean, median, and percentages.
  • Data Presentation: Converting data into understandable formats like charts, graphs, and tables that allow easy interpretation.
Statistics help in understanding the viability of collected data and in extracting useful insights. It can be pivotal in fields like science, business, economics, and any area where data-driven decisions are necessary.

Understanding the basics of statistics is crucial when interpreting data visualizations such as pie charts and bar charts. These visual tools succinctly convey statistical results, making complex data more tangible and easier to read for a general audience.

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