Question 1: A bar chart shows the number of students choosing different sports: Soccer (15), Basketball (20), Tennis (10), and Swimming (25). Identify the mistake if the chart's y-axis is labeled from 0 to 25 in increments of 5, but the bars for Tennis and Swimming are incorrectly scaled.

Answer: The bar for Tennis appears taller than the bar for Swimming, which is incorrect because Tennis has fewer students (10) than Swimming (25). The mistake is the inconsistent scaling or plotting error.

Question 2: Given a bar chart where the height of the bar for 'Apples' is 12 units and 'Oranges' is 8 units, and the scale is 1 unit = 2 students, how many students preferred each fruit?

Answer: Apples: 24 students, Oranges: 16 students

Question 3: A bar chart shows data with categories A, B, C, D. The bars for categories B and D are of equal height, but the bar for C is noticeably shorter. If the total number of responses is 100, and categories A and C together account for 40 responses, what can you infer about the distribution of responses?

Answer: Since B and D are equal and C is shorter, A and C total 40 responses, so B and D together make up 60 responses. B and D each have approximately 30 responses, indicating a relatively even distribution between B and D with fewer for C.

Question 4: A student claims that a bar chart with a higher bar for 'Fruits' than 'Vegetables' always means more people prefer Fruits. Is this statement correct? Explain your reasoning.

Answer: Not necessarily. The height of the bar depends on the scale used and plotting accuracy. Without verifying the data, we cannot assume the actual number of people prefers Fruits over Vegetables.

Question 5: A bar chart shows the following data: Red (8), Blue (12), Green (8), Yellow (4). The chart's y-axis is divided from 0 to 15 in increments of 3. Which category is most likely misrepresented if the bars appear to be of equal height?

Answer: The categories Red and Green both have 8 units of data; if their bars appear equal, no misrepresentation. But if Blue is supposed to be higher than Red and Green but appears similar, the mistake might be in scaling or plotting.

Question 6: Construct a bar chart to represent the following data: 10 students prefer Reading, 15 prefer Writing, 5 prefer Listening, and 20 prefer Speaking. Label the axes clearly and ensure proper scaling.

Answer: Student draws bars proportional to the data, with y-axis scaled so that 1 unit = 1 student, and labels both axes accordingly.

Question 7: In a bar chart, the category 'Cats' has a bar height of 7 units, and 'Dogs' has 14 units. If the scale is 1 unit = 3 animals, how many animals preferred each pet?

Answer: Cats: 21 animals, Dogs: 42 animals

Question 8: A bar chart shows data with an error: the total count of responses sums to 70, but the chart indicates a total of 80. What common mistake could this be, and how should it be corrected?

Answer: The mistake is likely incorrect scaling or misreading the data. To correct, verify the actual data points and ensure the bars accurately reflect the counts.

Question 9: Explain why it is important to verify the scale and units when interpreting a bar chart. Provide an example where misinterpretation could lead to incorrect conclusions.

Answer: Verifying scale and units ensures accurate understanding of data. For example, if a chart uses 1 unit = 5 units of data but students assume 1 unit = 1, they may underestimate differences, leading to wrong conclusions.

Question 10: Identify the error in the following interpretation: A bar chart shows 'X' with 30 responses and 'Y' with 20 responses. The conclusion is that more people prefer 'X'. The error?

Answer: The interpretation is correct if the scales are consistent; no error. If the bars are scaled correctly, then 'X' is preferred by more people.