Question

Statistics of the world's religions are only approximate, because many religions do not keep track of their membership numbers. An estimate of these numbers (in millions) is shown in the table. \({ }^{11}\) $$ \begin{array}{lrlr} \hline \text { Religion } & \begin{array}{l} \text { Members } \\ \text { (millions) Religion } \end{array} & \begin{array}{l} \text { Members } \\ \text { (millions) } \end{array} \\ \hline \text { Buddhism } & 376 & \text { Judaism } & 14 \\ \text { Christianity } & 2,100 & \text { Sikhism } & 23 \\ \text { Hinduism } & 900 & \text { Chinese traditional } & 394 \\ \text { Islam } & 1,500 & \text { Other } & 61 \\ \text { Primal indigenous } & 400 & & \\ \text { and African } & & & \\ \text { traditional } & & & \\ \hline \end{array} $$ a. Use a pie chart to describe the total membership in the world's organized religions. b. Use a bar chart to describe the total membership in the world's organized religions. c. Order the religious groups from the smallest to the largest number of members. Use a Pareto chart to describe the data. Which of the three displays is the most effective?

Short answer

Answer: The Pareto chart is generally considered the most effective means of displaying the data on the total membership in the world's religions for this specific exercise because it combines the clear numerical differences of a bar chart with an additional line chart showing the cumulative percentage of membership, allowing for a more comprehensive visualization and interpretation of the data distribution and focus on the largest religious groups.

Step-by-step solution

a. Pie Chart

First, let's create a pie chart to represent the world's organized religions membership. To create a pie chart, we need to find the percentage share of each religious group. Calculate the total population by adding up the members of all religious groups: Total population = \(376 + 2100 + 900 + 1500 + 400 + 14 + 23 + 394 + 61 = 5768\) (in millions) Now find the percentage share of each group by dividing the number of members in each group by the total population and multiplying by 100: Buddhism: \(100 \times \frac{376}{5768} \approx 6.52\% \) Christianity: \(100 \times \frac{2100}{5768} \approx 36.40\%\) Hinduism: \(100 \times \frac{900}{5768} \approx 15.59\%\) Islam: \(100 \times \frac{1500}{5768} \approx 26.00\%\) Primal Indigenous and African Traditional: \(100 \times \frac{400}{5768} \approx 6.93\%\) Judaism: \(100 \times \frac{14}{5768} \approx 0.24\%\) Sikhism: \(100 \times \frac{23}{5768} \approx 0.40\%\) Chinese Traditional: \(100 \times \frac{394}{5768} \approx 6.83\%\) Other: \(100 \times \frac{61}{5768} \approx 1.06\%\) Using these percentage shares, create a pie chart with each religion represented by a slice proportional to its share in the total population.

b. Bar Chart

Creating a bar chart is more straightforward. Assign each religion its own category, and create a vertical bar that corresponds to the number of members (in millions). Plot the religions along the x-axis, and represent the membership figures along the y-axis by drawing bars of appropriate heights.

c. Pareto Chart and Comparison

First, sort the religions from smallest to largest membership number: 1. Judaism: 14 million 2. Sikhism: 23 million 3. Other: 61 million 4. Chinese Traditional: 394 million 5. Primal Indigenous and African Traditional: 400 million 6. Buddhism: 376 million 7. Hinduism: 900 million 8. Islam: 1,500 million 9. Christianity: 2,100 million A Pareto chart combines a bar chart and a line chart. Plot the ordered religions (from smallest to largest) along the x-axis and draw bars corresponding to the membership figures on the y-axis. Additionally, create a line chart to show the cumulative percentage (y-axis) of the number of members for each religion, starting from the smallest group to the largest. To determine which of the three displays is most effective, consider the information each chart conveys. The pie chart provides an easy visual comparison of the proportional sizes of each religious group, while the bar chart clearly displays the numerical differences. Lastly, the Pareto chart highlights the distribution in a clearer manner and can be used to focus on the largest religious groups. Considering information delivery and ease of interpretation, the Pareto chart is generally the most effective means of displaying this data for this specific exercise.

Key concepts

Understanding Pie Charts

A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In this case, we are visualizing the membership numbers of the world's organized religions. Each slice of the pie chart corresponds to a religion and represents its percentage share of the total population. This visual representation is particularly effective for showing the relative sizes of data categories.

To create a pie chart, the total value of all categories combined must first be calculated — the sum of all religious group memberships in this exercise. Then, the size of each slice is determined by calculating what fraction of the total each category represents, which is then multiplied by 100 to get a percentage. This exercise emphasizes that pie charts are intuitive for showing the part-to-whole relationship; however, when it comes to comparing individual groups, especially those with similar proportions, it can be slightly less effective than other chart types due to the difficulty in assessing the size of each slice.

Bar Charts and their Functionality

On the other hand, a bar chart is an excellent tool for comparing the differences between categories due to its simple and clear layout. It uses rectangular bars to represent different data points, with the length of each bar corresponding to its category's value.

In educational probability and statistics, bar charts are particularly helpful because they arrange data into an easy-to-read format, where each religion is assigned to an individual bar with the height representing the membership (in millions here). It allows students to quickly grasp high and low quantities and make direct comparisons between categories. Our exercise proves that bar charts can display absolute numbers effectively, giving a clear snapshot of the data at a single glance. This makes it a favored tool in many educational and business settings where precise data representation is crucial.

Pareto Charts for Prioritized Analysis

Lastly, introducing the Pareto chart, which is a specialized type of bar chart. A Pareto chart is particularly useful in displaying both frequency of occurrence and its cumulative impact. It is essentially a bar chart ordered in descending order of magnitude from left to right, with an overlaid line graph representing the cumulative total percentage.

As shown in the step-by-step solution for this exercise, religious groups are organized from the smallest number of members to the largest. The bar component of the Pareto chart shows the number of members in millions, and the line component demonstrates a cumulative percentage of the total population up to that point. This dual-purpose graph is valuable in educational contexts for its ability to identify the 'vital few' — a principle suggesting that most effects come from relatively few causes. In our religious membership analysis, a Pareto chart provides a hierarchical structure to the data, highlighting the most significant religions in terms of membership count, which offers deep insights into the distribution, potentially guiding where educational or social resources could be prioritized.