Question

Facebook Fanatics The social networking site called Facebook has grown quickly since its inception in 2004. In fact, Facebook's United States user base grew from 42 million users to 103 million users between 2009 and \(2010 .\) The table below shows the age distribution of Facebook users (in thousands) as it changed from January 2009 to January \(2010 .^{3}\) $$\begin{array}{lrc}\text { Age } & \text { As of 1/04/2009 } & \text { As of 1/04/2010 } \\\\\hline 3-17 & 5675 & 10,680 \\\8-24 & 17,192 & 26,076 \\\25-34 &11,255 & 25,580 \\\35-54 & 6989 & 29,918 \\\55+ & 955 & 9764 \\\\\text { Jnknown } & 23 & 1068 \\\\\hline \text { fotal } & 42,089 & 103.085 \\\\\hline\end{array}$$ a. Define the variable that has been measured in this table. b. Is the variable quantitative or qualitative? c. What do the numbers represent? d. Construct a pie chart to describe the age distribution of Facebook users as of January \(4,2009 .\) e. Construct a pie chart to describe the age distribution of Facebook users as of January \(4,2010 .\) f. Refer to parts \(\mathrm{d}\) and e. How would you describe the changes in the age distributions of Facebook users during this 1 -year period?

Short answer

Describe the changes in the age distributions of Facebook users during the 1-year period between January 4, 2009, and January 4, 2010. During this 1-year period, there was a noticeable shift in the age distribution of Facebook users, with the user base becoming older. The percentage of users in the age groups 3-17 and 18-24 decreased, while the percentage of users in age groups 35-54 and 55+ increased significantly. Additionally, there was a slight decrease in the percentage of users in the age group 25-34 and an increase in the percentage of users with an unknown age. The platform attracted more users from older age groups, indicating a diversification of its user base.

Step-by-step solution

a. Define the variable that has been measured in this table.

The variable that has been measured in this table is the age distribution of Facebook users in different age groups.

b. Is the variable quantitative or qualitative?

The variable is quantitative, as the age distribution can be measured and expressed in numerical values.

c. What do the numbers represent?

The numbers in the table represent the number of Facebook users (in thousands) in each age group as of January 4, 2009, and January 4, 2010.

d. Construct a pie chart to describe the age distribution of Facebook users as of January 4, 2009.

1. Calculate the percentage of each age group as a proportion of the total number of users in 2009: 3-17: (5675/42089) * 100 = 13.48% 18-24: (17192/42089) * 100 = 40.85% 25-34: (11255/42089) * 100 = 26.75% 35-54: (6989/42089) * 100 = 16.61% 55+: (955/42089) * 100 = 2.27% Unknown: (23/42089) * 100 = 0.05% 2. Create a pie chart with the following labels and percentages: 3-17: 13.48% 18-24: 40.85% 25-34: 26.75% 35-54: 16.61% 55+: 2.27% Unknown: 0.05%

e. Construct a pie chart to describe the age distribution of Facebook users as of January 4, 2010.

1. Calculate the percentage of each age group as a proportion of the total number of users in 2010: 3-17: (10680/103085) * 100 = 10.36% 18-24: (26076/103085) * 100 = 25.30% 25-34: (25580/103085) * 100 = 24.80% 35-54: (29918/103085) * 100 = 29.03% 55+: (9764/103085) * 100 = 9.47% Unknown: (1068/103085) * 100 = 1.04% 2. Create a pie chart with the following labels and percentages: 3-17: 10.36% 18-24: 25.30% 25-34: 24.80% 35-54: 29.03% 55+: 9.47% Unknown: 1.04%

f. Refer to parts d and e. How would you describe the changes in the age distributions of Facebook users during this 1-year period?

Comparing the pie charts of 2009 and 2010, we can observe the following changes in the age distribution of Facebook users: - The percentage of users in the age group 3-17 decreased from 13.48% to 10.36%. - The percentage of users in the age group 18-24 also decreased from 40.85% to 25.30%. - The percentage of users in the age group 25-34 slightly decreased from 26.75% to 24.80%. - The percentage of users in the age group 35-54 increased significantly from 16.61% to 29.03%. - The percentage of users in the age group 55+ also increased significantly from 2.27% to 9.47%. - The percentage of users with an unknown age increased from 0.05% to 1.04%. In summary, there is a noticeable shift in the age distribution, with the user base becoming older with more users from age groups 35-54 and 55+ joining Facebook during this period.

Key concepts

Quantitative Variable

When analyzing data like the Facebook age distribution, an important aspect is understanding the nature of the variable measured. Here, the variable is the age distribution of Facebook users. This variable is quantitative because it represents numerical data—specifically, the number of users in each age bracket. Quantitative variables can be expressed in numbers and usually allow for mathematical computations. In this scenario, each age group is associated with a distinct numerical value indicating the thousands of users in each group, both for 2009 and 2010. Such data helps target analysis, allowing us to compare, calculate growth rates, and understand demographic shifts over time.

Pie Chart Construction

Pie charts are a visually appealing way to represent data proportions, making them easy to understand at a glance. Constructing a pie chart involves transforming numerical data into percentages. Here is a step-by-step process for constructing the pie chart of Facebook's age distribution for any given year:

• Calculate the percentage of each category by dividing the number of users in each age group by the total number of users, then multiply by 100 to get a percentage.
• Each percentage corresponds to a "slice" of the pie chart, where the sum of all slices equals 100%.
• Label each slice with the correct age group and percentage to facilitate interpretation.

By visualizing this data in pie charts for 2009 and 2010, users can quickly see which age groups comprise larger or smaller portions of the user base and how these proportions have shifted over time.

Data Interpretation

Once a pie chart is constructed, interpreting the data it represents becomes the next critical step. In our scenario comparing Facebook's user age distribution between 2009 and 2010, several trends can be observed:

• A decline in the proportion of users aged 3-17 suggests a drop-off in younger users, from 13.48% to 10.36%.
• The most significant shift is seen in the 35-54 age group, which nearly doubled in proportion, signifying the platform's growing popularity among older adults.
• The age group 18-24 still holds a substantial share but dropped from 40.85% to 25.30%, possibly indicating a slight migration to other platforms or a diversification of user ages in Facebook's demographics.

Data interpretation allows educators, marketers, and analysts to formulate strategies based on observed trends, enhancing decision-making informed by demographic changes.

Social Media Trends

The rapid evolution of social media platforms like Facebook affects and reflects wider societal trends. Between 2009 and 2010, Facebook saw a pronounced demographic shift. Initially popular among younger users, it expanded to attract a broader, older audience. This trend indicates several possible influences:

• Older generations are increasingly adopting digital platforms for social interaction.
• Younger demographics might be exploring newer platforms, leading to a relative decrease in their Facebook usage.
• Overall user base growth could mean specific targeting strategies worked effectively to include a wider audience.

Understanding these trends is critical for businesses and individuals alike. It helps in crafting relevant content, undertaking marketing initiatives, and designing applications that resonate with the evolving user base.