Data handling and analysis：練習問題

Find the median of the following set of scores:
12, 18, 11, 14, 15, 19, 14

The table below shows the number of goals scored by a soccer team in 20 matches.

Goals: 0, 1, 2, 3
Frequency: 4, 7, 6, 3

Calculate the mean number of goals scored per match.

A set of \( n \) observations has a mean of \( \bar{x} \) and a standard deviation of \( \sigma \). If each observation is multiplied by 2 and then decreased by 3, what are the new mean and the new standard deviation?

A box-and-whisker plot was drawn to represent the marks of a class of students. If the lower quartile is 45 and the upper quartile is 72, what is the interquartile range of the marks?

In a histogram, the class interval \( 20 < x \le 30 \) has a frequency density of 1.2. The class interval \( 30 < x \le 50 \) has a frequency density of 0.8. Calculate the total frequency for the range \( 20 < x \le 50 \).

The marks of 9 students in a mathematics quiz are: 12, 15, 18, 14, 20, 15, 22, 19, and 15. Determine the median and the mode of this set of data.

A set of five numbers has a mean of \( 8 \) and a standard deviation of \( 2 \). If a sixth number, \( k \), is added to the set, the new mean becomes \( 9 \). Calculate the value of \( k \) and find the new standard deviation, leaving your answer to 2 decimal places.

The number of goals scored by a school soccer team in 20 matches is recorded in the table below.

Goals: 0, 1, 2, 3, 4
Frequency: 4, 5, 6, 3, 2

(a) Calculate the mean and the standard deviation of the goals scored.
(b) In the previous season, the mean was \( 1.5 \) and the standard deviation was \( 1.1 \). State whether the team performed better and if their performance was more consistent this season.

A group of 40 students sat for a mathematics test. Their marks are summarized in the table below:

Marks (\(x\)): \(0 \le x < 20\), \(20 \le x < 40\), \(40 \le x < 60\), \(60 \le x < 80\), \(80 \le x < 100\)
Frequency (\(f\)): 2, 8, 12, 14, 4

(a) Calculate an estimate for the mean mark and the standard deviation of the test results.
(b) The same group of students took a second test. For the second test, the mean was 62 and the standard deviation was 15.6. Compare the performance of the students in the two tests in two ways.