Worked example · Digital Media and Film · Year 11
LNF: Numeracy → Learning that statistics represent data and that probability models chance helps us make informed inferences and decisions → Interpreting data
A secure Year 11 response, annotated so you can see which success criterion each part meets. It is also the answer key. Weekend falls: 33.5%, 37.2%, 46.1%, 56.1%, 61.1%. Opening weekend = 29.7% of the total. Per screen: £1,300, £791.67, £583.33. Mean views: 158.3 thousand (series 1) and 225.5 thousand (series 2), an increase of 42.4%. Episode 5 kept 65.2% and 78.8% of episode 1’s views. The press release bar looks 6 times taller, but the real increase is 23.8%. Either product can be judged more successful in Step 5 if the judgement uses the figures and admits the limits of the data. All figures are invented practice data.
| From | Working | Percentage fall |
|---|---|---|
| Weekend 1 to 2 | (182 − 121) ÷ 182 × 100 | 33.5% |
| Weekend 2 to 3 | (121 − 76) ÷ 121 × 100 | 37.2% |
| Weekend 3 to 4 | (76 − 41) ÷ 76 × 100 | 46.1% |
| Weekend 4 to 5 | (41 − 18) ÷ 41 × 100 | 56.1% |
| Weekend 5 to 6 | (18 − 7) ÷ 18 × 100 | 61.1% |
(b) 182,000 ÷ 612,000 × 100 = 29.7%. Almost a third of all the money came in the first 3 days.
(c) Weekend 1: 182,000 ÷ 140 = £1,300. Weekend 3: 76,000 ÷ 96 = £791.67. Weekend 6: 7,000 ÷ 12 = £583.33. No: even per screen, takings fell by more than half (from £1,300 to £583.33, a fall of 55.1%), so each screen was selling fewer tickets. Fewer people wanted to see the film, not just fewer places to see it.
Percentage change is always calculated from the earlier value. The falls get steeper every week, which is itself a finding. Part (c) separates two possible causes with a calculation. Evidences criteria 1, 2 and 5.
(a) Series 1: 210 + 168 + 150 + 141 + 137 + 144 = 950; 950 ÷ 6 = 158.3 thousand. Series 2: 260 + 231 + 219 + 212 + 205 + 226 = 1,353; 1,353 ÷ 6 = 225.5 thousand.
(b) (225.5 − 158.3) ÷ 158.3 × 100 = 42.4% increase (using 158.33 unrounded gives the same answer to 1 decimal place).
(c) Series 1: 137 ÷ 210 × 100 = 65.2%. Series 2: 205 ÷ 260 × 100 = 78.8%. Series 2 kept a much bigger share of the people who started it, which suggests viewers found it more gripping, not just that more people tried it.
(d) Episode 6 is the finale: people who had drifted away come back to find out how it ends, and the service may promote the final episode.
Uses unrounded values in the percentage so rounding does not creep in. Part (c) goes beyond the headline average to look at audience retention, a better sign of whether viewers enjoyed the series. Evidences criteria 1, 2 and 5.
(a) The axis starts at 200. The series 1 bar is 210 − 200 = 10 units tall and the series 2 bar is 260 − 200 = 60 units tall, so it looks 6 times taller.
(b) (260 − 210) ÷ 210 × 100 = 23.8%. Series 2’s first episode had about a quarter more views, not six times as many. Starting the vertical axis at 200 instead of 0 cuts off most of each bar, so a small difference looks huge. The word “exploded” adds to the effect.
Quantifies how the chart misleads (6 times against 1.24 times) and names the technique: a truncated axis. Evidences criteria 1 and 3.
| Claim | What the data supports | What it cannot show, and what else I would want |
|---|---|---|
| “The film was a failure.” | Box office of £612,000 is only 43.7% of the £1.4 million budget (612,000 ÷ 1,400,000 × 100), and cinemas keep part of it. | It shows cinema tickets only. I would want TV, streaming and overseas sales, the value of the festival award, and what the company expected the film to earn. |
| “over a million viewers” | There were 1,353,000 views of series 2 episodes in 28 days. | Views are not viewers: one account watching all 6 episodes counts 6 times, and 2 minutes counts as a view. Episode 1 had 260,000 views, so there were probably nearer 260,000 accounts. One account may also be a family. I would want unique viewers and how many watched to the end. |
Why a direct comparison is hard: the two products are measured in different units, money for the film and views for the series; the time periods differ (10 weeks against 28 days); and we have no figure for what Sgrin paid for the series, so we cannot compare income.
Accepts what each figure shows, then explains precisely what it cannot show and what data would settle the question. Evidences criteria 4 and 5.
On the evidence available, Y Ffin series 2 was the more successful product for Ffilmiau Hafod, although the comparison is not straightforward. Y Chwarel opened strongly, but its takings fell every weekend, by 33.5% after the first weekend and by 61.1% by the sixth. Takings per screen fell from £1,300 to £583, so audiences were shrinking, not just screens. Its £612,000 box office is only 43.7% of its £1.4 million budget, and cinemas keep part of that. However, the board has no figures for television or streaming sales, so we cannot yet call the film a failure. Y Ffin series 2 averaged 225.5 thousand views per episode, a 42.4% rise on series 1, and episode 5 kept 78.8% of the episode 1 audience, compared with 65.2% for series 1. Views are not viewers, though: one account watching 6 episodes counts 6 times, and 2 minutes counts as a view. Even so, the series grew and held its audience, while the film lost its audience quickly, so Y Ffin was the more successful product.
173 words. Uses nine calculated figures, admits two limitations (missing income data; views are not viewers) and still reaches a clear judgement, with the reason stated in the final sentence. It says how certain the conclusion is (“on the evidence available”). Evidences criteria 2, 4 and 5.