Histograms, cumulative frequency and box plots (Higher)：練習問題

The time taken, \(t\) minutes, for 80 students to finish a puzzle is recorded.
The cumulative frequency graph shows that the median is 15 minutes, the lower quartile is 11 minutes, and the upper quartile is 19 minutes.
The fastest time was 5 minutes and the slowest time was 30 minutes.
Calculate the interquartile range of the times.

The table shows the weights of 60 apples.
\(80 < w \le 100\): 10 apples
\(100 < w \le 110\): 25 apples
\(110 < w \le 120\): 15 apples
\(120 < w \le 150\): 10 apples
Which interval contains the median weight?

The frequency density for a class interval \(20 < w \le 50\) in a histogram is \(1.2\).
The total frequency for this interval is represented by a bar with a width of \(3\text{ cm}\) and a height of \(6\text{ cm}\) on a specific scale.
Calculate the frequency of this class interval.

The table shows information about the heights of 40 plants.
\(0 < h \le 10\): 8 plants
\(10 < h \le 20\): 13 plants
\(20 < h \le 30\): 12 plants
\(30 < h \le 40\): 7 plants
Calculate an estimate for the mean height of the plants.

A set of data consists of 5 positive integers: \(n, n+2, n+2, n+3, n+11\).
The mean of these 5 integers is equal to the median.
Find the value of \(n\).

A team played 20 matches. The number of goals scored in these matches were: 0 goals in 5 matches, 1 goal in 7 matches, 2 goals in 6 matches, and 3 goals in 2 matches.
Calculate the mean number of goals scored per match.

A company manufactures light bulbs. The lifetime of a light bulb is measured in hours. A sample of 100 bulbs has a mean lifetime of 1200 hours and a standard deviation of 50 hours.
A second sample of 100 bulbs from a different machine has a mean lifetime of 1250 hours and a standard deviation of 120 hours.
Compare the two distributions by making two distinct points of comparison.

The weights of 20 students in Class A are recorded. The median is \( 55 \text{ kg} \), the lower quartile is \( 48 \text{ kg} \), and the upper quartile is \( 62 \text{ kg} \). The range is \( 28 \text{ kg} \) and the lightest student is \( 42 \text{ kg} \).

(a) Draw a box plot for Class A.
(b) Class B has a median weight of \( 52 \text{ kg} \) and an interquartile range of \( 10 \text{ kg} \). Compare the distributions of weights for Class A and Class B.

The table shows information about the weights of 60 parcels.

Weight (\( w \) kg) | Frequency
\( 0 < w \leq 2 \) | 12
\( 2 < w \leq 3 \) | 15
\( 3 < w \leq 5 \) | 18
\( 5 < w \leq 8 \) | 15

(a) Calculate the frequency densities for the histogram.
(b) Estimate the number of parcels with a weight greater than \( 4 \text{ kg} \).