Measure of Central Tendency：練習問題

Find the median of the following set of scores: \(12, 7, 10, 8, 14\).

The mean of five consecutive even integers is \(M\). What is the value of the smallest of these five integers in terms of \(M\)?

The estimated mean of the following grouped frequency distribution is \(27\). Find the missing frequency \(k\):

Class Interval | Frequency
\(10 - 19\) | \(4\)
\(20 - 29\) | \(k\)
\(30 - 39\) | \(6\)
\(40 - 49\) | \(2\)

The mean of a data set is \(45\). If each value in the data set is multiplied by \(3\), what is the new mean?

The following table shows the scores of \(40\) students in a quiz:

Score | 0 | 1 | 2 | 3 | 4 | 5
Frequency | 3 | 7 | 12 | 8 | 5 | 5

Find the median score of the students.

The heights of five students are measured as \(148\) cm, \(152\) cm, \(145\) cm, \(155\) cm, and \(h\) cm. If their mean height is \(150\) cm, find the value of \(h\).

A set of five distinct positive integers has a mean of \(20\) and a median of \(18\). If the mode does not exist and the largest integer in the set is \(32\), find the maximum possible value of the second largest integer.

The table below shows the frequency distribution of the weights of \(30\) packages.

Weight (kg) | Frequency
\(0 - 10\) | \(4\)
\(10 - 20\) | \(a\)
\(20 - 30\) | \(b\)
\(30 - 40\) | \(6\)

If the estimated mean weight of the packages, calculated using class marks, is exactly \(22\text{ kg}\), find the values of \(a\) and \(b\).

A group of 8 students recorded the number of books they read during the summer holidays:

(a) Find the mean of the number of books read.

(b) Find the mode of the data set.

(c) Find the median of the data set.

A student's final grade in a mathematics course is calculated using a weighted mean. The weights for three components are as follows:

In the first semester, Kelvin scored 90 in Homework and 70 in the Mid-term Exam.

(a) If Kelvin scores 82 in the Final Exam, calculate his overall weighted mean score.

(b) If Kelvin wants to achieve an overall weighted mean score of at least 85, find the minimum score he must obtain in the Final Exam.