Statistics 简明教程
Statistics - Continuous Series Arithmetic Mean
当数据根据范围及其频率给出时。以下是连续序列的一个例子：
Items |
0-5 |
5-10 |
10-20 |
20-30 |
30-40 |
Frequency |
2 |
5 |
1 |
3 |
12 |
In case of continous series, a mid point is computed as $\frac{lower-limit + upper-limit}{2}$ and Arithmetic Mean is computed using following formula.
Formula
其中——
-
${N}$ = Number of observations.
-
${f_1,f_2,f_3,…,f_n}$ = 频率 f 的不同值。
-
${m_1,m_2,m_3,…,m_n}$ = Different values of mid points for ranges.
Example
Problem Statement −
Let’s calculate Arithmetic Mean for the following continous data −
Items |
0-10 |
10-20 |
20-30 |
30-40 |
Frequency |
2 |
5 |
1 |
3 |
Solution −
根据给定的数据，我们有−
Items |
Mid-pt |
Frequency |
${fm}$ |
0-10 |
5 |
2 |
10 |
10-20 |
15 |
5 |
75 |
20-30 |
25 |
1 |
25 |
30-40 |
35 |
3 |
105 |
${N=11}$ |
${\sum fm=215}$ |
根据上面提到的公式，算术平均值 $\bar{x}$ 为−
给定数字的算术平均值为 19.54。