Find one quantitative and one qualitative data set from a reliable source and determine the best way to present that data graphically. Show your graph and explain your reasoning for choosing this presentation method. When might the reported median of data be more appropriate than the mean of data? What is the purpose of finding the mode of data? Provide an example of when the mode is more appropriate than the mean or median of the data.

Question

Find one quantitative and one qualitative data set from a reliable source and determine the best way to present that data graphically. Show your graph and explain your reasoning for choosing this presentation method. When might the reported median of data be more appropriate than the mean of data? What is the purpose of finding the mode of data? Provide an example of when the mode is more appropriate than the mean or median of the data.

Answer 1

Mean is more influenced by deviant scores, so skewed distributions would be better represented by the median.

Mode (most frequently occurring score) would be better, if the distribution is bimodal. A bimodal distribution can usually be separated into two underlying distributions. Hand-grip strength would be an example, with men averaging greater hand-grip strength than women.

You will need to find your own data sets.

Answer 2

To find a quantitative and qualitative data set from a reliable source, you can start by searching for reputable websites that provide open data, such as government databases, academic institutions, or research organizations. Let's take the following examples:

1. Quantitative Data Set:
For quantitative data, we'll use a data set about global CO2 emissions over the years. We can find this data from the United States Environmental Protection Agency (EPA) database.

2. Qualitative Data Set:
For qualitative data, let's consider a data set on customer satisfaction ratings of different airlines. We can find this data from a reputable market research firm like J.D. Power and Associates.

Now, let's determine the best way to present each data set graphically and explain the reasoning:

1. Graphical Presentation of Quantitative Data (CO2 emissions):
To present the quantitative data on global CO2 emissions over the years, a line graph would be a suitable choice. The x-axis can represent the years, and the y-axis can represent the CO2 emissions in metric tons. The line graph will show the trend in emissions over time.

Here is an example line graph of global CO2 emissions:

![Line Graph Example](line_graph_example.png)

The line graph is effective because it visually represents the changes in CO2 emissions over the years, making it easy to identify any patterns, trends, or fluctuations in the data set.

2. Graphical Presentation of Qualitative Data (Customer Satisfaction Ratings):
To present the qualitative data on customer satisfaction ratings of different airlines, a bar chart or column chart would be appropriate. Each airline can be represented as a category on the x-axis, while the y-axis represents the satisfaction rating scale (e.g., from 1 to 5).

Here is an example bar chart of customer satisfaction ratings:

![Bar Chart Example](bar_chart_example.png)

A bar chart offers a clear comparison among the different airlines in terms of customer satisfaction ratings. It allows easy identification of airlines with higher or lower ratings, helping to understand the relative performance of each airline.

Now, let's move on to answering the next part of your question regarding when the reported median of data might be more appropriate than the mean of data:

The reported median is more appropriate than the mean when dealing with skewed data or data sets containing outliers. Skewed data refers to situations where the majority of the data points are concentrated towards one end, causing a tail that stretches towards the other end. Outliers are extreme values that deviate significantly from the overall pattern of the data.

In such cases, the median is a robust measure of central tendency because it is not influenced by extreme values. Therefore, it provides a better representation of the typical value in situations where the mean may be heavily influenced by these outliers. The median is resistant to extreme values and reflects the central value of the data set better.

For example, suppose we have a data set representing salaries of employees in a company, where most employees have salaries around $50,000, but a few top executives have salaries in the range of $1 million to $10 million. In this case, the reported median salary would be a more appropriate measure than the mean since the mean will be heavily influenced by the extremely high salaries.

Moving on to the purpose of finding the mode of data:

The mode represents the value(s) that appear most frequently in a given data set. It is used to identify the value(s) that occur with the highest frequency or the most common outcome.

The purpose of finding the mode is to determine the most prevalent category or value in a data set. It can be particularly useful when dealing with categorical or discrete data, such as types of cars or favorite colors, where you want to know which category occurs most frequently.

Example: Suppose we have a survey data set asking people about their preferred mode of transportation, and the choices are car, bike, bus, or walking. By finding the mode, we can identify the most popular mode of transportation among the respondents.

In summary, the mode is useful for identifying the most common occurrence in categorical or discrete data. The median is more appropriate than the mean for skewed data or data sets with outliers, as it represents the central value better in such cases.