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 −

  1. ${N}$ = Number of observations

  2. ${f_1,f_2,f_3,…​,f_n}$ = Different values of frequency f.

  3. ${x_1,x_2,x_3,…​,x_n}$ = 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.

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