Observed vs Expected Frequencies
Calculate Expected Frequency
Calculate the expected number of times each outcome occurs.
Fair coin flipped 100 times. Expected heads = ___
Fair die rolled 60 times. Expected 3s = ___
4-section spinner, 80 spins. Expected per section = ___
5 colours, 200 draws. Expected per colour = ___
More Expected Frequencies
Calculate expected frequency.
Die rolled 120 times. Expected 6s = ___
Coin flipped 50 times. Expected tails = ___
3-section spinner, 90 spins. Expected per section = ___
4 colours, 100 draws. Expected per colour = ___
Match Expected to Experiment
Match each experiment to its expected result.
Expected Frequency Check
Circle the correct expected frequency.
Die 30 times. Expected 1s:
Coin 200 times. Expected heads:
5-spinner 100 times. Per section:
8 colours 160 draws. Per colour:
Using the Formula
Expected = trials × probability.
P(heads) = 1/2, 80 flips. Expected heads = ___
P(even) = 1/2, 60 rolls. Expected even = ___
P(red) = 1/4, 100 draws. Expected red = ___
P(A) = 3/8, 80 spins. Expected A = ___
Compare Observed and Expected
Die rolled 60 times. Expected per number = 10. Observed: 1→8, 2→12, 3→10, 4→15, 5→7, 6→8.
Above expected: ___
Below expected: ___
Die unfair? Explain: ___
Is This Expected?
Fair coin, 100 flips.
52 heads, 48 tails
85 heads, 15 tails
47 heads, 53 tails
70 heads, 30 tails
More Expected vs Unexpected
Die rolled 60 times (expected 10 per number).
11 threes
2 fives
9 ones
25 sixes
Spinner Analysis
4 equal sections, 100 spins: A=28, B=22, C=26, D=24.
Expected per section: ___
Above expected: ___
Spinner likely fair? ___
Comparing Trial Sizes
Think about how trial count affects results.
10 flips, 7 heads. Coin unfair? ___
1,000 flips, 700 heads. Coin unfair? ___
Why is the second more convincing? ___
Investigate the Results
3 equal sections (R, B, G), 90 spins: R=35, B=25, G=30.
Expected per colour: ___
Most observed? Significantly more? ___
Spinner unfair? What would help decide? ___
With 900 spins, closer to expected? Explain: ___
Law of Large Numbers
Explain in your own words.
What happens to observed frequencies with more trials? ___
Why is this useful? Give an example: ___
Why does a casino rely on this law? ___
Design an Investigation
Design an experiment to test if a coin is fair.
How many flips? ___
Results that suggest fair: ___
Results that suggest unfair: ___
How to display results: ___
Home Activity: Frequency Investigator
Test whether your results match expected!
- 1Flip a coin 50 times. Compare to expected 25 heads.
- 2Roll a die 36 times. Each number about 6 times?
- 3Try with 100 rolls. Closer to expected?
- 4Discuss: why do more trials give closer results?
- 5Create a table: expected vs observed for your experiment.
Match the Vocabulary
Match each term to its definition.
Calculate Expected and Observed
A spinner has 4 equal sections: red, blue, green, yellow. Spun 100 times.
Expected frequency of red = ___
Observed red: 28. Difference from expected = ___
Observed blue: 22. Relative frequency = ___
Which colour had results closest to expected? ___
Die Roll Frequency Chart
Expected: each face appears about 17 times in 100 rolls. Record the observed results.
| Item | Tally | Total |
|---|---|---|
Face 1 | ||
Face 2 | ||
Face 3 | ||
Face 4 | ||
Face 5 | ||
Face 6 |
Analyse the Die Roll Results
Use the tally chart above to answer these questions.
Which face appeared most? ___
Biggest difference between observed and expected: ___
Does this mean the die is unfair? ___
What would happen if you rolled 1,000 times? ___
Interpret the Gap
Circle the best interpretation.
Expected 50 heads, got 44 in 100 flips:
Expected 17 sixes, got 17 in 100 rolls:
As trials increase, observed frequency:
A large difference in a small experiment means:
Observed vs Expected Comparison
Graph shows observed coin flips per experiment. Each star = 10 flips. Expected heads = 50%. Answer the questions.
| Trial 1 (100) | |
| Trial 2 (100) | |
| Trial 3 (200) | |
| Trial 4 (500) | |
| Trial 5 (1000) |
Which trial got exactly 50% heads?
Which varied most from 50%?
What trend appears as trials increase?
Relative Frequency Table
Complete this table: a die rolled 60 times.
Expected frequency of each face = ___
Expected relative frequency = ___
Face 3 appeared 12 times. Relative frequency = ___
Difference between observed and expected relative frequency for face 3 = ___
Sort by Reliability
Sort each experiment by how reliable its results are.
Coin Experiment Design
Design and record a coin experiment.
Number of flips: ___
Expected heads: ___
Observed heads: ___
Observed relative frequency: ___
How does this compare to P = 0.5? ___
Order of Analysis Steps
Put the steps in order for comparing observed to expected frequency.
Spinner Fairness Test
A spinner has 3 sections: A, B, C. Spun 90 times: A=35, B=28, C=27.
Expected frequency of each = ___
Biggest difference = ___
Do you think the spinner is fair? ___
How many more spins would help you decide? ___
Frequency Totals
The observed frequencies must add to the total trials. Find the missing value.
Biased or Fair?
For each experiment, say whether the die/coin/spinner is likely biased.
Die rolled 600 times: face 6 appeared 180 times. Expected: 100. Biased? ___
Coin flipped 200 times: 102 heads. Biased? ___
Spinner 3 sections, 150 spins: A=80, B=40, C=30. Biased? ___
Medical Statistics Application
A new drug is tested on 1,000 people. 200 recover (expected: 150 without drug).
Expected frequency with no drug = ___
Observed frequency with drug = ___
Does the drug appear to help? ___
Why is a large sample important in medical research? ___
Match Frequency Formulas
Match each term to its formula.
Create an Experiment Record Sheet
Design a table to record an experiment comparing observed and expected.
Column headings for your table: ___
What probability experiment would you choose? ___
How many trials and why? ___
Observed vs Expected Summary
Summarise everything you have learned.
Expected frequency = ___
Observed frequency = ___
Law of large numbers means: ___
A real-world example where this comparison matters: ___
One question you would like to investigate: ___