Identify the scenarios in which the statistics are misleading.

Question

A supermarket claims that 65% of its shoppers would like to see home delivery offered. They arrived at the conclusion by polling 50 randomly selected customers on a Tuesday afternoon.
A music store owner claims that about 15% of high school students in his city can play the piano. He concludes this after surveying 80 randomly selected students from the various high schools in his city.
A website claims that 47% of its visitors click on at least one advertisement while browsing the site. The information was collected from a database containing all the activity on the website during the past month.
A report by a company that manufactures hair brushes says 56% of people who buy their brushes own only one hair brush. The conclusion comes from a survey of 500 males who bought the company's brush.
A clothing store claims that 45% of its customers prefer skinny jeans over regular jeans. They concluded this from a survey which asked 120 randomly selected teenage customers which style they prefer.

Answer 1

To identify the scenarios in which the statistics might be misleading, we can analyze the methodology and population surveyed for each claim:

1. Supermarket Claim: The supermarket polled 50 randomly selected customers on a Tuesday afternoon. This could be misleading since the sample size is relatively small, and the time of polling (Tuesday afternoon) might not represent the entire customer base, which could vary throughout the week.

2. Music Store Owner: The music store owner surveyed 80 randomly selected students from various high schools in the city. While the sample size isn't extremely small, the claim's validity depends on how "random" the selection was and whether these students represent the broader demographic of high school students in the city. If the survey excluded certain high schools or types of students, the results could be misleading.

3. Website Claim: The website reports that 47% of its visitors click on at least one advertisement based on a database of activity over the past month. This could be misleading because it does not provide context on user behavior — for example, it does not account for users who might not interact with ads at all or those who visit multiple times.

4. Hair Brush Manufacturer: The company surveyed 500 males who bought their brushes and concluded that 56% own only one hairbrush. The statistic might be misleading because it is based solely on customers who purchased their specific product. The sample is not representative of the general population and does not consider the behavior of people who may use brushes from other brands.

5. Clothing Store: The clothing store claims that 45% of its customers prefer skinny jeans over regular jeans based on a survey of 120 randomly selected teenage customers. This could be misleading because the specific demographic (teenage customers) may not be representative of all customers purchasing jeans. Additionally, "preference" can be influenced by trends that fluctuate rapidly.

Based on this analysis, the first, second, fourth, and fifth scenarios contain elements that may lead to misleading conclusions due to small sample sizes, sample bias, lack of representativeness, or specificity to certain demographics. The third scenario is less likely to be misleading if the database was comprehensive, though its interpretation also depends on understanding user behavior more fully.