Question

Facebook and age Refer to the preceding exercise.

Part (a). Find the distribution of Facebook use for each of the three age groups. Make a segmented bar graph to compare these distributions.

Part (b). Describe what the graph in part (a) reveals about the association between age and Facebook use.

Short answer

Part (a)

	Younger	Middle	Older
Yes	95.12%	70%	31.34%
No	4.88%	30%	68,66%

Part (b)

Yellow part of the graph

Facebook use appears to be decreasing as people get older.

The majority of younger and middle school students use Facebook, while the majority of older students do not.

Step-by-step solution

Part (a) Step 1. Given information

The following two-way table displays data for the 219 students who responded to the survey.

Part (a) Step 2. To compare these distributions, create a segmented bar graph.

First, compute the row/column totals of the given table, which are the sum of all counts in the row/column:

	Younger	Middle	Older	Row total
Yes	78	49	21	78+49+21=148
No	4	21	46	4+21+46=71
Column total	4+78=82	49+21=70	21+46=67	148+71=219

We divide the counts by the column total to determine the distribution of Facebook use by age group.

	Younger	Middle	Older
Yes	$\frac{78}{82}=95.12\%$	$\frac{49}{70}=70\%$	$\frac{21}{67}=31.34\%$
No	$\frac{4}{82}=4.88\%$	$\frac{21}{70}=30\%$	$\frac{46}{67}=68.66\%$

Each bar's width must be the same, and its height must be equal to the percentage.

As a result:

	Younger	Middle	Older
Yes	95.12%	70%	31.34%
No	4.88%	30%	68,66%

Part (b) Step 1. Yellow part of the graph in part (a) shows about the relationship between age and Facebook use.

We can see that as people get older, their use of Facebook appears to decrease, as the area of the yellow section of the bars shrinks.

Furthermore, because the corresponding bars have a larger yellow area than the green area, the majority of the younger and middle students use Facebook. However, because the corresponding bars have a larger green area than a yellow area, the majority of the older students do not use Facebook.

As a result:

Facebook use appears to be decreasing as people get older.

The majority of younger and middle school students use Facebook, while the majority of older students do not.