Analyse data：练习题

A small boutique records its sales over four days:
Day 1: \(50\) units
Day 2: \(25\) units
Day 3: \(25\) units
Day 4: \(100\) units

If this information is represented in a pie chart, what is the angle of the sector representing Day 4?

A company compares its regional sales for two years using a stacked bar chart. In \(2021\), Region A sold \(100\) units and Region B sold \(200\) units. In \(2022\), Region A sold \(150\) units and Region B sold \(120\) units.

Which of the following is a correct observation when transforming this table into the stacked bar chart?

The volume of water in a storage tank is monitored over time. From \(0\) to \(5\) minutes, the volume increases at a constant rate from \(100\) L to \(300\) L. From \(5\) to \(10\) minutes, the volume continues to increase at a constant rate, reaching \(400\) L at the \(10\)-minute mark.

What is the most likely explanation for the change in the graph's gradient at \(t = 5\)?

A meteorologist records monthly rainfall for a city: January: \(10\) mm, February: \(15\) mm, March: \(20\) mm, and April: \(25\) mm.

Which linear model correctly represents the rainfall \(R\) (in mm) based on the month number \(n\), where January is \(n=1\)?

A graph shows the distance a cyclist travels over a period of \(30\) minutes. The line is straight and sloping upwards from \(t = 0\) to \(t = 10\) minutes, becomes perfectly horizontal from \(t = 10\) to \(t = 20\) minutes, and then slopes upwards again from \(t = 20\) to \(t = 30\) minutes.

Which of the following is the most likely explanation for the trend between \(t = 10\) and \(t = 20\)?

In a small competition, the top three scores were 95, 88, and 82. The range of all six participants was 25. What is the lowest possible score achieved in the competition?<\/p>

A survey of 200 people showed that 120 prefer tea, 100 prefer coffee, and 40 prefer both. How many people surveyed prefer neither tea nor coffee?<\/p>

A city's bike-sharing usage data shows a strong positive correlation between temperature and the number of rentals. However, when the temperature exceeds \(35^\circ \text{C}\), the number of rentals drops sharply.

Suggest a plausible reason for this non-linear trend and explain how a researcher could modify a simple linear model to better represent this change in the data pattern.

The following table shows the number of visitors to a local museum over four months:

January: 1200
February: 1500
March: 1800
April: 2100

The museum manager claims that the number of visitors is increasing by a constant percentage each month.
a) Use the data to show whether the manager's claim of a constant percentage increase is correct.
b) If the trend in the number of additional visitors per month continues linearly, how many visitors should be expected in May?

The height of water in a rectangular storage tank was recorded over 40 minutes as it was being filled. For the first 10 minutes, the height increased at a constant rate from \(0\) cm to \(30\) cm. At \(t = 10\) minutes, a second identical pipe was opened, and the filling continued until \(t = 25\) minutes. At that point, both pipes were closed, and a drain was opened that emptied the tank at a rate of \(3\) cm per minute until the tank was empty.

a) What was the height of the water at \(t = 25\) minutes?
b) Determine the rate of increase in water height (in cm/min) between \(t = 10\) and \(t = 25\).
c) At what time \(t\) will the tank be completely empty?