Limits and reliability of predictions

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Quick Questions

Shade in the A or B circle for each question.

1. A student predicts next year's canteen sales using only 3 days of data. How reliable is the prediction?

A Not very reliable, because the sample is too small

B Very reliable, because any data makes a good prediction

2. Which dataset gives a more reliable trendline for predicting test scores?

A Scores from 200 students over 3 years

B Scores from 4 students on one day

3. One student's data point is far above all the others and drags the trendline upward. What is it called, and what should you do?

A An outlier: check it and see how much it changes the prediction

B A trend: ignore the other points and follow it

4. Your data covers Years 1 to 5 of a school's enrolments. Which prediction is more reliable?

A Predicting enrolments for Year 50

B Predicting enrolments for Year 6

5. Which statement about a prediction is better practice?

A "Sales will be exactly 120. The trendline proves it."

B "Sales will likely be about 120, but this is uncertain because we only have 6 months of data."

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1=FORECAST(30, B2:B6, A2:A6)		APredicting 40 years beyond the data is extrapolating too far, and 'exactly' ignores uncertainty.
2=FORECAST(100, B2:B20, A2:A20)		BA sample of 3 points is too small to be certain. The claim of 100% confidence ignores how unreliable small samples are.
3Stating uncertainty: give a prediction as a range, not one exact number		CA prediction made from only 5 data points, so it has low reliability and should be stated with caution
4Effect of an outlier: one extreme value can drag the trendline and make the prediction less reliable		DSlope with outlier: 9.5 \| Slope without: 2.1
5Using 3 data points, I am 100% sure next year's result will be 52.		EA prediction far beyond the data range (x values only go up to about 20), so confidence in it is low
6Data covers 2015-2020, so the trendline proves the 2060 population is exactly 8.4 million.		FPredicted sales: 120 (likely between 100 and 140)

Definitions

reliability

Fill in the Blanks

Complete each line of code by filling in the missing parts.

=________(12,B2:B11,A2:A11)

=_____(B2:B6)

IF samples _ 10 THEN confidence ← "low"

=______(B2:B11)

______ "Estimate only, not certain"

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A n ← COUNT(B2:B31)

B IF n > 10 THEN

C note ← "Low confidence"

D ELSE note ← "Fairly reliable"

Question 2

A scores ← [52,55,58,54,300]

B avg ← AVERAGE(scores)

C med ← MEDIAN(scores)

D SAY "Average resists outliers"

Question 3

A pred ← 412

B margin ← 30

C SAY "412 exactly, no doubt"

Question 4

A sample ← 4 students

B trend ← rises each week

C predict ← next week higher

D SAY "High confidence: tiny n"

Question 5

A x ← months 1 to 10

B y ← sales, one spike of 900

C Spike has no effect on trend

D Check the trend without it

Answer Key

Limits and reliability of predictions

Section A: Quick Questions

A — Not very reliable, because the sample is too small

A — Scores from 200 students over 3 years

A — An outlier: check it and see how much it changes the prediction

B — Predicting enrolments for Year 6

B — "Sales will likely be about 120, but this is uncertain because we only have 6 months of data."

Section B: Match the Pairs

=FORECAST(30, B2:B6, A2:A6) → A prediction made from only 5 data points, so it has low reliability and should be stated with caution

=FORECAST(100, B2:B20, A2:A20) → A prediction far beyond the data range (x values only go up to about 20), so confidence in it is low

Stating uncertainty: give a prediction as a range, not one exact number → Predicted sales: 120 (likely between 100 and 140)

Effect of an outlier: one extreme value can drag the trendline and make the prediction less reliable → Slope with outlier: 9.5 | Slope without: 2.1

Using 3 data points, I am 100% sure next year's result will be 52. → A sample of 3 points is too small to be certain. The claim of 100% confidence ignores how unreliable small samples are.

Data covers 2015-2020, so the trendline proves the 2060 population is exactly 8.4 million. → Predicting 40 years beyond the data is extrapolating too far, and 'exactly' ignores uncertainty.

Section C: Definitions

reliability — How much you can trust a prediction. It drops with small samples, outliers and predicting far beyond your data, so always state how uncertain the prediction is.

Section D: Fill in the Blanks

=FORECAST(12,B2:B11,A2:A11)

=COUNT(B2:B6)

IF samples < 10 THEN confidence ← "low"

=MEDIAN(B2:B11)

OUTPUT "Estimate only, not certain"

Section E: Spot the Error

B — A small sample means low confidence, so the test should be n < 10. With n > 10 the rule flags large samples as low confidence, which is backwards.

D — The outlier 300 drags the average up, but the median stays steady. It is the median that resists outliers, not the average.

C — A prediction should state its uncertainty, for example 'give or take 30'. Claiming it is exact with no doubt overstates how reliable it is.

D — A sample of only 4 is too small to trust a trend. The confidence should be low, not high.

C — An outlier can pull a trendline towards it and change the predictions. It should say the spike pulls the trendline up.