Averages：練習問題

A set of data consists of 7 numbers: 14, 22, 14, 18, 25, 14, and 20. Find the difference between the mean and the mode of this set of data.

The weights of 6 students are 42 kg, 45 kg, 48 kg, 50 kg, 45 kg, and \(x\) kg. If the mean weight is equal to the mode weight, what is the value of \(x\)?

A group of students were surveyed about their study hours. The mean study time for 15 boys is 4 hours, and the mean study time for 10 girls is 6.5 hours. If one more girl who studies for 9 hours joins the group, what is the new mean study time for the whole group?

A bar chart shows the favorite fruits of a group of 40 students. 12 students chose Apple, 10 chose Orange, 8 chose Banana, and the rest chose Pear. Which fruit represents the mode of the dataset?

The median of five consecutive odd integers is 21. What is the mean of these five integers?

The scores of four students in a test are 68, 75, 82, and 75. If a fifth student joins and the mean score of the five students becomes 76, what is the score of the fifth student?

In a mathematics quiz, the scores of five students are 72, 85, 91, 64, and 78. If a sixth student takes the quiz and the median score of all six students remains unchanged from the median of the original five students, find the possible integer score of the sixth student.

The weights of four students are \(38\text{ kg}\), \(42\text{ kg}\), \(45\text{ kg}\), and \(38\text{ kg}\).
(a) Find the mode of the weights.
(b) Find the mean weight of the students.

A group of 6 students took a mathematics quiz. Their scores were 78, 85, 92, 78, 90, and 81.
(a) Find the mean score of the group.
(b) Find the median score of the group.
(c) What is the mode of the scores?

The following data shows the scores of five students in a Mathematics test: 74, 82, 85, 74, and 90.
(a) Find the mean score of the five students.
(b) After a sixth student, Kevin, takes the test, the new mean score of the group becomes 81. What was Kevin's score?
(c) Find the median and the mode of the scores of all six students.