初中 · 數學
5 道选择题即时批改，另有 5 道文字题附完整解题步骤，全部围绕「統計簡介」。
The frequency of the number of pets owned by \(20\) families is recorded as follows:
Number of pets: \(0\), Frequency: \(4\)
Number of pets: \(1\), Frequency: \(9\)
Number of pets: \(2\), Frequency: \(5\)
Number of pets: \(3\), Frequency: \(2\)
Find the mode of the number of pets owned.
The following stem-and-leaf diagram shows the daily steps (in hundreds) of a person over \(15\) days.
Daily Steps (Hundreds)
Stem | Leaf
4 | 2 5 8
5 | 0 1 3 3 7 9
6 | 2 4 5 5 8 8
Key: \(4 | 2\) represents \(4200\) steps. Find the range of the steps.
The table below shows the frequency distribution of the scores of \(50\) students in a test.
| Score (\(x\)) | Frequency |
|---|---|
| \(0 \le x < 10\) | 5 |
| \(10 \le x < 20\) | 12 |
| \(20 \le x < 30\) | 18 |
| \(30 \le x < 40\) | 10 |
| \(40 \le x < 50\) | 5 |
A researcher records the heights of several trees in a park. Which type of data is being collected?
In a school's grading system, the final grade is calculated as a weighted mean: the final exam accounts for \(60\%\), the midterm for \(30\%\), and homework for \(10\%\). If a student scores \(70\) in the exam, \(80\) in the midterm, and \(90\) in homework, what is the student's weighted mean score?
Is the height of students in a class an example of discrete or continuous data?
先自己写一遍答案，再对照解题步骤。
Classify the following two data sets as either discrete or continuous: (i) the number of goals scored by a team in a football season, and (ii) the weight of a baby recorded at birth. Explain your reasoning briefly.
先自己写一遍答案，再对照解题步骤。
The mean height of \( 12 \) plants is \( 25 \text{ cm} \). If one plant with a height of \( 14 \text{ cm} \) is replaced by a new plant that is \( 32 \text{ cm} \) tall, what is the new mean height of the plants?
先自己写一遍答案，再对照解题步骤。
For each of the following measurements, state whether the data collected is discrete or continuous, and provide a brief explanation for your choice:
(a) The mass (in kilograms) of babies born in a hospital over a week.
(b) The number of cars passing through a toll booth per hour.
(c) The time spent by a student completing a homework assignment.
先自己写一遍答案，再对照解题步骤。
The cumulative frequency table below shows the marks scored by 80 candidates in an English examination.
| Mark (\(x\)) | Cumulative Frequency |
|---|---|
| \(x < 20\) | 8 |
| \(x < 40\) | 25 |
| \(x < 60\) | 55 |
| \(x < 80\) | 70 |
| \(x < 100\) | 80 |
(a) Determine the number of candidates who scored marks between \(40\) and \(79\).
(b) State the class interval that contains the median mark.
(c) Estimate the value of the lower quartile (\(Q_1\)). (Assume linear interpolation within the class interval.)
先自己写一遍答案，再对照解题步骤。
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