Past exam of the digital social research: statistics core course of the University of Oxford / 2020 / 2 / Solution

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 visible age rows, ages 25–44 form the largest group, with $562/1730\approx 32.49\%$, and ages 14–24 the smallest, with $182/1730\approx 10.52\%$. 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 $459/1424\approx 32.23\%$, 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 $566/1424\approx 39.75\%$ of valid responses using social media at least daily. The same recorded responses are $566/2053\approx 27.57\%$ of all listed cases. The second percentage is the fraction recorded as daily users, not an estimate that classifies all missing responses as nonusers. Missing social media responses make up $629/2053\approx 30.64\%$. 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. The substantive distributional summary must retain both the valid-response denominator and the missing-data qualification.