Statistics 简明教程
Discrete Series Arithmetic Mean
当数据与其频率一起给出时。以下是离散序列的一个例子 −
When data is given along with their frequencies. Following is an example of discrete series −
Items |
5 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
Frequency |
2 |
5 |
1 |
3 |
12 |
0 |
5 |
7 |
对于离散数列，可以使用以下公式来计算算术平均值。
For discrete series, the Arithmetic Mean can be calculated using the following formula.
Formula
或者，我们可以按以下方式编写相同的公式：−
Alternatively, we can write same formula as follows −
其中——
Where −
-
${N}$ = Number of observations
-
${f_1,f_2,f_3,…,f_n}$ = Different values of frequency f.
-
${x_1,x_2,x_3,…,x_n}$ = Different values of variable x.
Example
Problem Statement −
Problem Statement −
计算以下离散数据的算术平均值−
Calculate Arithmetic Mean for the following discrete data −
Items |
14 |
36 |
45 |
70 |
Frequency |
2 |
5 |
1 |
3 |
Solution −
Solution −
根据给定的数据，我们有−
Based on the given data, we have −
Items |
Frequency |
${fx}$ |
14 |
2 |
28 |
36 |
5 |
180 |
45 |
1 |
45 |
70 |
3 |
210 |
|
${N=11}$ |
${\sum fx=463}$ |
根据上面提到的公式，算术平均值 $\bar{x}$ 为−
Based on the above mentioned formula, Arithmetic Mean $\bar{x}$ will be −
给定数字的算术平均值为 42.09。
The Arithmetic Mean of the given numbers is 42.09.