Question

the table below shows the 3 most popular social media platforms and the distribution of the ages on those platforms. the data is based on mau (monthly active users). a random sample of 100 active users from each the platforms is taken and their age was recorded.

age group|social media platform|total
---|---|---

facebook

youtube

whatsapp

0 - 17|6|23|17|46
18 - 26|28|40|18|86
27 - 35|37|30|28|95
36 - 49|23|5|17|45
50 and older|6|2|20|28

100

100

100

300

create a mosaic plot of the data above. show all work and calculations used to create the plot.

Explanation:

Step1: Calculate row - percentages

For each age - group, divide the number of users in each platform by the total number of users in that age - group.
For age group \(0 - 17\):
Facebook percentage: \(\frac{6}{46}\times100\approx13.04\%\)
YouTube percentage: \(\frac{23}{46}\times100 = 50\%\)
WhatsApp percentage: \(\frac{17}{46}\times100\approx36.96\%\)
For age group \(18 - 26\):
Facebook percentage: \(\frac{28}{86}\times100\approx32.56\%\)
YouTube percentage: \(\frac{40}{86}\times100\approx46.51\%\)
WhatsApp percentage: \(\frac{18}{86}\times100\approx20.93\%\)
For age group \(27 - 35\):
Facebook percentage: \(\frac{37}{95}\times100\approx38.95\%\)
YouTube percentage: \(\frac{30}{95}\times100\approx31.58\%\)
WhatsApp percentage: \(\frac{28}{95}\times100\approx29.47\%\)
For age group \(36 - 49\):
Facebook percentage: \(\frac{23}{45}\times100\approx51.11\%\)
YouTube percentage: \(\frac{5}{45}\times100\approx11.11\%\)
WhatsApp percentage: \(\frac{17}{45}\times100\approx37.78\%\)
For age group \(50\) and older:
Facebook percentage: \(\frac{6}{28}\times100\approx21.43\%\)
YouTube percentage: \(\frac{2}{28}\times100\approx7.14\%\)
WhatsApp percentage: \(\frac{20}{28}\times100\approx71.43\%\)

Step2: Determine the width and height of each rectangle for the mosaic plot

The total number of observations is \(n = 300\).
We will represent the age - groups as vertical segments and the platforms within each age - group as horizontal segments.
The height of each age - group segment can be proportional to the number of users in that age - group. For example, the height of the \(0 - 17\) age - group segment can be set to \(46\) (relative units), the \(18 - 26\) age - group segment to \(86\) (relative units), etc.
Within each age - group, the width of the rectangles for Facebook, YouTube, and WhatsApp will be proportional to the percentages calculated in Step 1.

To actually create the mosaic plot, we can use software like R (using the ggplot2 package with the geom_mosaic() function), Python (using matplotlib with appropriate add - ons for mosaic plots), or Excel (with some custom formatting and calculations for the segment sizes).

However, the above calculations provide the necessary data to construct the mosaic plot where the rectangles are sized according to the proportion of users in each platform within each age - group.

Answer:

The above calculations (row - percentages and relative segment sizes) are the work needed to create the mosaic plot. The actual plot would be a visual representation with rectangles sized as per the calculated proportions, with age - groups on the vertical axis and platforms within each age - group on the horizontal axis.