Measures of Central Tendency and Dispersion：練習問題

The weights (in kg) of five students are 42, 45, 48, 50, and 55. What is the mean weight of these students?

The frequency distribution table below shows the scores of a group of students in a quiz:
Score: 2, 4, 6, 8
Frequency: 3, 5, 2, 2
Find the weighted mean score of the group.

A set of data consists of the following numbers: 7, 12, 12, 15, 18, 20, 22. What is the median of this data set?

The mean of five integers \(x, 14, 18, 21,\) and \(27\) is \(19\). If a sixth number, \(31\), is added to the data set, find the new mean.

A student records the number of books read by each classmate over the holidays: \(3, 8, 4, 6, 8, 2, 8, 5, 4\). What is the mode of this data set?

A set of data consists of five integers: \( 4, 7, 9, 12, \) and \( x \). If the mean of this data set is \( 8 \), find the value of \( x \).

If the mean of the data set \( 7, 14, x, 2x, \) and \( 15 \) is \( 12 \), find the value of \( x \).

Consider the following frequency distribution table for a set of continuous data:
Class \( [0, 10) \): Frequency \( 4 \)
Class \( [10, 20) \): Frequency \( k \)
Class \( [20, 30) \): Frequency \( 10 \)
If the estimated mean of the distribution is \( 17 \), find the value of \( k \).

A group of 10 students took a mathematics quiz. Their scores out of 10 are listed below:
7, 8, 5, 9, 6, 8, 10, 7, 8, 4

(a) Find the mean score of the students.
(b) Determine the mode of the scores.
(c) Find the median score.

A data set consists of \( 25 \) observations with a mean of \( 48 \) and a standard deviation of \( 6 \).
(a) Calculate the sum of all \( 25 \) observations.
(b) If each observation in the data set is multiplied by \( 1.5 \) and then increased by \( 5 \), determine the new mean and the new standard deviation of the data set.