Uses and abuses of statistics：練習問題

Which type of statistical chart is specifically used to show trends or continuous changes in data over a period of time, such as the change in hourly temperature of a city?

Study the broken line graph below. Why might a reader get a misleading impression about the trend of sales between the third and fourth data points?

Look at the bar chart below. Why is this chart misleading when comparing the values shown for the two categories?

A library recorded the total number of books borrowed in each of the five different categories last month. Which type of chart is best suited for comparing these quantities?

A survey was conducted to find the favorite fruit of \( 100 \) students. If we want to represent the proportion of the whole group that chose each fruit, which type of chart is most appropriate?

Which statistical chart is most suitable for showing the change in the average monthly temperature of Hong Kong over the past 12 months?

In a bar chart comparing two items, Item A has 105 units and Item B has 110 units. If the y-axis is broken and starts at 100, how many times taller will the bar for Item B appear compared to Item A?

A health drink company presents a pictogram showing their sales compared to a competitor. In their chart, the height of a bottle icon representing their sales is twice as tall as the competitor's icon. However, they also doubled the width of their icon to maintain the bottle's shape.

(a) Explain why this pictogram is an abuse of statistics and how it misleads the reader.
(b) If the actual sales values were \(2000\) bottles and \(1000\) bottles, which chart type would be most appropriate to compare these values fairly without visual distortion?

A company produces a bar chart to show their growth. The bar for this year is twice as wide and twice as tall as the bar for last year.
(a) If the height represents the profit, how many times has the profit actually increased?
(b) Why is increasing the width of the bar an abuse of statistics?

A researcher wants to know the average height of primary school students in a city. He decides to only measure the students on the school basketball team.
(a) Is this a biased or unbiased way to collect data?
(b) If the researcher presents this average as the average for the whole school, explain why this is an abuse of statistics.