📊 Part 1: Spotting Data Deceptions
1. Look at this claim: "90% of people prefer our chocolate!" Which question should you ask to check if this is misleading?
How many people were surveyed?
(Sample Answer: This question checks the sample size, which is crucial for understanding the validity of the claim.)
What colour is the chocolate?
How much does the chocolate cost?
Where is the chocolate made?
2. A graph shows test scores from 85% to 90%. What makes this graph potentially misleading?
The scale doesn't start at zero
(Sample Answer: Starting the scale above zero can exaggerate differences and mislead viewers about the actual performance.)
The numbers are too high
There are too many colours
The graph is too small
3. Which of these could make a statistic misleading? (Tick all that apply)
Very small sample size
(Sample Answer: A small sample size may not represent the larger population accurately.)
Biased survey questions
(Sample Answer: Biased questions can lead to skewed results that do not reflect true opinions.)
Using bright colours
Cherry-picking data
(Sample Answer: Cherry-picking data involves selecting only favorable data points, which can mislead the audience.)
4. A company surveys 5 of their own employees and claims "100% of people love working here!" Why is this misleading?
(Sample Answer: The sample size is too small and biased, as it only includes employees who may feel pressured to give positive feedback.)
📈 Part 2: Measures of Centre
5. The heights (in cm) of Year 5 students are: 142, 145, 143, 150, 145, 148, 145
a) Mean = _______ cm (Sample Answer: Mean = (142 + 145 + 143 + 150 + 145 + 148 + 145) / 7 = 145 cm)
b) Median = _______ cm (Sample Answer: Median = 145 cm (middle value when arranged in order: 142, 143, 145, 145, 145, 148, 150))
c) Mode = _______ cm (Sample Answer: Mode = 145 cm (most frequently occurring height))
6. A shop owner wants to show that their prices are low. They have items costing: $2, $3, $4, $5, $95. Which measure of centre should they use and why?
Mean, because it includes all prices
(Sample Answer: The mean would be skewed by the $95 item, making it misleading.)
Median, because it's not affected by the expensive item
(Sample Answer: The median is the best choice as it represents the middle value without being affected by the outlier.)
Mode, because it's the most common price
All three are equally good
7. Test scores: 65, 70, 72, 75, 98. A teacher wants to show the class performed well. Which average would make the class look best?
The mean because it includes all scores and gives a higher average due to the high score of 98, but it may not represent the overall performance accurately.
🎯 Part 3: Creating Persuasive Data
8. You want to convince your parents that you should get more pocket money. You earn $5 per week, but your three friends earn $8, $10, and $12. How would you present this data persuasively?
(Sample Answer: I would show that my friends earn significantly more than I do, highlighting that I am at a disadvantage compared to them.)
9. A school wants to show improvement in reading scores over 4 years: 75%, 76%, 77%, 78%. Describe two ways they could make this improvement look more dramatic in a graph.
(Sample Answer: 1. Use a non-zero baseline to exaggerate the differences. 2. Use a larger scale for the y-axis to make small increases appear larger.)
10. Create a misleading headline about this data: "In a survey of 1000 people, 510 preferred Brand A chocolate, 490 preferred Brand B."
Misleading headline: "Brand A Dominates Chocolate Preferences!"
Why is it misleading? It suggests a significant preference for Brand A, while the difference is only 20 people, which is not a large margin in a survey of 1000.
