Cumulative Frequency and Box Plots：練習題

The five-number summary of a dataset of student heights (in cm) is given by: Minimum \( = 145 \), Lower Quartile \( Q_1 = 152 \), Median \( = 160 \), Upper Quartile \( Q_3 = 168 \), and Maximum \( = 180 \). What is the interquartile range (IQR) of this dataset?

Refer to the cumulative frequency polygon below showing the distribution of running times (in minutes) for 120 athletes.

What is the estimate for the 60th percentile of the running times?

Refer to the cumulative frequency curve below showing the examination marks of 160 students.

If the passing mark is set such that the top 25% of students pass the examination, what is the minimum mark required to pass?

Refer to the box plot shown below representing the daily study hours of a class of students.

Which of the following statements is correct?

A dataset consists of 11 positive integers arranged in ascending order: \( 4, 6, 7, 9, x, 14, 16, 18, 20, 22, y \).
The median is \( 12 \) and the interquartile range (IQR) is \( 11 \). If \( y \) is an upper outlier according to the \( 1.5 \times \text{IQR} \) rule, what is the smallest possible integer value of \( y \)?

A box-and-whisker plot for a set of data has a minimum value of 14, a lower quartile of 22, a median of 31, an upper quartile of 45, and a maximum value of 58. Calculate the interquartile range (IQR) and range of the data set.

The box plots below represent the test scores for Class A and Class B. Which class has the higher median score, and which class has a smaller interquartile range (IQR)?

The cumulative frequency graph below shows the distribution of test scores for 200 students. Based on the graph, determine the number of students who achieved a score between the 30th percentile and the 75th percentile.

The box plot below summarizes the daily study time (in minutes) of a group of students.

(a) State the median and the interquartile range (IQR) of the daily study time.
(b) Determine whether a daily study time of 150 minutes would be classified as an outlier. Justify your answer with calculations.

The cumulative frequency curve below illustrates the distribution of weights (in kg) of 120 athletes.

(a) Using the curve, estimate:
(i) the median weight.
(ii) the interquartile range (IQR).
(b) An athlete is classified as 'Heavyweight' if their weight is in the top \(15\%\) of the group. Find the minimum weight required to be classified as 'Heavyweight'.
(c) Two athletes are chosen at random without replacement from those weighing 70 kg or less. Given that 48 athletes weigh 60 kg or less and 84 athletes weigh 70 kg or less, find the probability that both chosen athletes weigh more than 60 kg.