Solution (source code)

= Solution

\b[Employment is observed for all 2053 listed cases. <Social media> use is observed for 1424 cases, with 629 missing. The age <percentages> describe the five visible rows, whose counts total 1730; they cannot be treated as a complete age distribution for the stated 2053 cases.]

A <frequency table> describes category counts and their <relative frequencies>. The full-sample <percentage> uses every listed case as denominator; a <valid percentage> excludes <missing data> for that variable. A <cumulative percentage> adds the <valid percentages> up to an ordered category. The denominator matters as much as the number: a statement about respondents with recorded use need not describe every respondent.

Employment is a <binary categorical variable>: 1216 cases are employed and 837 are not, or about $59.23\%$ and $40.77\%$. Neither employment category is missing in this output. Employment labels have no intrinsic numerical spacing; codes zero and one identify the two categories under a chosen ordering convention. <Cumulative percentages> for a <nominal categorical variable> depend on the arbitrary display order and add little to this two-category description.

Age groups are an <ordinal categorical variable> because their <intervals> have a natural ordering, although the grouped representation loses exact ages. Among the five \i[visible] age rows, ages 25–44 form the largest group, with $562/1730\approx32.49\%$, and ages 14–24 the smallest, with $182/1730\approx10.52\%$. The other visible groups account for $20.98\%$, $16.42\%$ and $19.60\%$ on that denominator. About $43.01\%$ of the visible five-row count is below 45. These <percentages> should not be silently applied to the stated total $2053$: for example, the same $562$ cases are only $27.37\%$ of $2053$.

The age variable key advertises six categories, whereas only five appear. Their counts sum to $1730$, leaving a difference of $323$ against the printed total; the table nevertheless prints zero missing values. This is an internal source discrepancy, not permission to label those $323$ cases as a particular unseen age group or as recorded <missing data>. The oldest row is labelled 65+ here but 65–74 in Figure 2. Even the age <percentage> total has a small display discrepancy: the five rounded <percentages> sum to $100.01\%$, while the printed valid total and last <cumulative percentage> say $99.99\%$. The much larger count inconsistency remains after allowing ordinary rounding.

<Social media> use is also an <ordinal categorical variable>. Its six ordered categories express increasing frequency, not equally spaced measurements: averaging category labels or claiming a one-unit change has a constant time meaning would require an additional scoring convention. Among the $1424$ observed responses, the <mode> is never, at $459/1424\approx32.23\%$, followed by daily, at $28.37\%$. Weekly use accounts for $18.19\%$, use more than once a day for $11.38\%$, less-than-monthly use for $6.39\%$, and monthly use for $3.44\%$. The first three categories together comprise about $42.06\%$ of valid responses. Consequently the middle ordered response lies in the weekly category: cumulative frequency first passes one half there.

Combining the two daily categories gives $566/1424\approx39.75\%$ of valid responses using <social media> at least daily. The same recorded responses are $566/2053\approx27.57\%$ of all listed cases. The second <percentage> is the fraction \i[recorded] as daily users, not an estimate that classifies all missing responses as nonusers. Missing <social media> responses make up $629/2053\approx30.64\%$. The directly calculated valid fraction is $69.36\%$; summing the individually rounded full-sample <percentages> produces the printed $69.37\%$, a minor rounding difference. With no account of the <missing-data mechanism>, the observed valid distribution should not automatically be generalized to those with missing use. Employment being fully observed does not make <social media> missingness ignorable. \b[The substantive distributional summary must retain both the valid-response denominator and the missing-data qualification.]