Worked example · Digital Technology · Year 10
LNF: Numeracy → Learning that statistics represent data and that probability models chance helps us make informed inferences and decisions → Interpreting data
A complete, secure Year 10 answer, annotated so you can see which success criterion each part meets. It is also the answer key. Headline figures: 60% of visitors booked on a phone; minutes to book have a mean of 10.25, a median of 9, a mode of 9 and a range of 40; without the outlier the mean is 8.42 and the range 7; mean ratings are phone 3.75, tablet 6.00, laptop 7.40; 50% want better online booking. This is practice with an invented client, not NEA. The most common mistake is finding the median without putting the values in order first.
| Device | Tally | Frequency | Percentage |
|---|---|---|---|
| Phone | |||| |||| || | 12 | 12 ÷ 20 × 100 = 60% |
| Tablet | ||| | 3 | 15% |
| Laptop | |||| | 5 | 25% |
| Total | 20 | 100% |
The frequencies add to 20 and the percentages to 100%, which checks the count. Evidences criterion 1.
(a) 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 12, 12, 45
| Statistic | Working | Answer |
|---|---|---|
| Mean | Total 205 ÷ 20 | 10.25 minutes |
| Median | 20 values, so halfway between the 10th and 11th: 9 and 9 | 9 minutes |
| Mode | 9 appears 4 times, more than any other value | 9 minutes |
| Range | 45 − 5 | 40 minutes |
Check the total: the 19 values without 45 add to 160, and 160 + 45 = 205. Evidences criterion 2.
(a) 45 minutes, visitor 10. Their comment says the website froze twice and they had to start again, so it is not a normal booking time.
(b) Mean = 160 ÷ 19 = 8.421… = 8.42 minutes. Range = 12 − 5 = 7 minutes.
(c) The median (9 minutes). The single value of 45 pulls the mean up to 10.25, which is more than 15 of the 20 people took. The median hardly changes with or without the outlier (9 both times), so it describes a typical visitor better.
(d) No. It should be left out of the averages, but it is still evidence: the old website can crash during booking, which the new website must fix.
The answer shows the effect of the outlier on the mean and the range and uses it to justify the choice of average. Part (d) treats the outlier as information, not a mistake. Evidences criterion 3.
| Device | Mean rating (working) | Mean rating | Mean minutes (working) | Mean minutes |
|---|---|---|---|---|
| Phone | 4 + 3 + 5 + 3 + 4 + 5 + 1 + 4 + 5 + 4 + 3 + 4 = 45; 45 ÷ 12 | 3.75 | 108 ÷ 11 (outlier left out) | 9.82 |
| Tablet | 6 + 6 + 6 = 18; 18 ÷ 3 | 6.00 | 7 + 8 + 9 = 24; 24 ÷ 3 | 8.00 |
| Laptop | 7 + 8 + 7 + 8 + 7 = 37; 37 ÷ 5 | 7.40 | 6 + 5 + 6 + 5 + 6 = 28; 28 ÷ 5 | 5.60 |
(b) The smaller the screen, the worse the experience. Phone users rate the website only 3.75 out of 10 and take 9.82 minutes to book, whereas laptop users rate it 7.40 and take 5.60 minutes. This suggests the website does not work well on phones, even though 60% of visitors use one.
The pattern is described with numbers from both ends and linked back to Step 1, which turns two statistics into a finding. Evidences criterion 4.
| Most wanted feature | Frequency | Percentage |
|---|---|---|
| Online booking | 10 | 50% |
| Prices | 4 | 20% |
| Photos and videos | 3 | 15% |
| Weather | 3 | 15% |
3 + 3 + 4 + 10 = 20 and 15 + 15 + 20 + 50 = 100. Evidences criterion 1.
(a)
(b) Only 20 people answered, so one or two unusual answers can change the percentages a lot (each person is 5%). Everyone was asked at reception, so the survey only includes people who managed to book; people who gave up on the website are missing, and they might be the ones with the worst experience.
Every decision follows the frame and rests on at least one statistic. The limitations explain how each could make the conclusion wrong. Evidences criteria 5 and 6.