Mô -đun thống kê cung cấp các công cụ rất mạnh mẽ, có thể được sử dụng để tính toán bất cứ điều gì liên quan đến số liệu thống kê. Phương sai [] là một trong các hàm như vậy. Hàm này giúp tính toán phương sai từ một mẫu dữ liệu [mẫu là một tập hợp con của dữ liệu dân cư]. & NBSP; Chức năng phương sai [] chỉ nên được sử dụng khi phương sai của mẫu cần được tính toán. Có một hàm khác được gọi là pvariance [], được sử dụng để tính toán phương sai của toàn bộ dân số. Trong các thống kê thuần túy, phương sai là độ lệch bình phương của một biến so với giá trị trung bình của nó. Về cơ bản, nó đo lường sự lây lan của dữ liệu ngẫu nhiên trong một tập hợp từ giá trị trung bình hoặc trung bình của nó. Giá trị thấp cho phương sai chỉ ra rằng dữ liệu được nhóm lại với nhau và không được phân tách rộng rãi, trong khi giá trị cao sẽ chỉ ra rằng dữ liệu trong tập hợp đã cho nhiều hơn nhiều so với giá trị trung bình. & NBSP; Phương sai là một công cụ quan trọng trong Các ngành khoa học, trong đó phân tích thống kê dữ liệu là phổ biến. Đó là bình phương độ lệch chuẩn của bộ dữ liệu đã cho và còn được gọi là thời điểm trung tâm thứ hai của phân phối. Nó thường được đại diện bởi & nbsp; trong thống kê thuần túy. Varariance được tính bằng công thức sau: & nbsp; & nbsp;variance[] is one such function. This function helps to calculate the variance from a sample of data [sample is a subset of populated data].
variance[] function should only be used when variance of a sample needs to be
calculated. There’s another function known as pvariance[], which is used to calculate the variance of an entire population.
In pure statistics, variance is the squared deviation of a variable from its mean. Basically, it measures the spread of random data in a set from its mean or median value. A low value for variance indicates that the data are clustered together and are not spread apart widely, whereas a high value would indicate that the data in the given set are much more spread apart
from the average value.
Variance is an important tool in the sciences, where statistical analysis of data is common. It is the square of standard deviation of the given data-set and is also known as second central moment of a distribution. It is usually represented by
Variance is calculated by the following formula :
Nó được tính toán theo giá trị trung bình của hình vuông bình phương trung bình & nbsp;
Cú pháp: Phương sai [[Dữ liệu], Xbar] Tham số: & nbsp; [Dữ liệu]: Một số lặp có số có giá trị thực. & NBSP; Xbar [Tùy chọn] Các giá trị được truyền dưới dạng tham số. Exexceptions: & nbsp; StatisticerError được nâng lên cho dữ liệu-set nhỏ hơn 2 giá trị được truyền dưới dạng tham số. & nbsp; variance[ [data], xbar ]
Parameters :
[data] : An iterable with real valued numbers.
xbar [Optional] : Takes actual mean of data-set as value.
Returntype : Returns the actual variance of the values passed as parameter.
Exceptions :
StatisticsError is raised for data-set less than 2-values passed as parameter.
Throws impossible values when the value provided as xbar doesn’t match actual mean of the data-set.
Mã số 1: & NBSP;
Python3
import
statistics
sample
=
[
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000060
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000062
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____14
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____16
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000068
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____11
Variance of Sample set is 0.36566666666666672
Variance of Sample set is 0.36566666666666673
Variance of Sample set is 0.36566666666666674
Variance of Sample set is 0.36566666666666675
Variance of Sample set is 0.36566666666666676
Variance of Sample set is 0.36566666666666677
Đầu ra: & nbsp; & nbsp;
Variance of sample set is 0.40924
& nbsp; & nbsp; mã số 2: trình bày phương sai [] trên một loạt các loại dữ liệu & nbsp; & nbsp;
Code #2 : Demonstrates variance[] on a range of data-types
Python3
Variance of Sample set is 0.36566666666666678
Variance of Sample set is 0.36566666666666679
import
0.36566666666630531
Variance of Sample set is 0.36566666666666678
0.36566666666630533
import
0.36566666666630535
Các
Các
Các
[
6=
[
8
0.36566666666630539
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____41
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000060222
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000611
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000612
Traceback [most recent call last]: File "/home/64bf6d80f158b65d2b75c894d03a7779.py", line 10, in print[statistics.variance[sample]] File "/usr/lib/python3.5/statistics.py", line 555, in variance raise StatisticsError['variance requires at least two data points'] statistics.StatisticsError: variance requires at least two data points3
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061
sample
2Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000602
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000617
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061
Traceback [most recent call last]: File "/home/64bf6d80f158b65d2b75c894d03a7779.py", line 10, in print[statistics.variance[sample]] File "/usr/lib/python3.5/statistics.py", line 555, in variance raise StatisticsError['variance requires at least two data points'] statistics.StatisticsError: variance requires at least two data points7
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000620
Các
Variance of Sample set is 0.36566666666666672
Variance of Sample set is 0.36566666666666673
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000636
Variance of Sample set is 0.36566666666666676
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000638
Variance of Sample set is 0.36566666666666672
Variance of Sample set is 0.36566666666666673
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000641
Variance of Sample set is 0.36566666666666676
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000643
Variance of Sample set is 0.36566666666666672
Variance of Sample set is 0.36566666666666673
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000646
Variance of Sample set is 0.36566666666666676
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000648
Variance of Sample set is 0.36566666666666672
Variance of Sample set is 0.36566666666666673
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000651
Variance of Sample set is 0.36566666666666676
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000653
Variance of Sample set is 0.36566666666666672
Variance of Sample set is 0.36566666666666673
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000656
Variance of Sample set is 0.36566666666666676
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000658
Đầu ra: & nbsp; & nbsp;
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.17613000000000006
& nbsp; & nbsp; mã số 2: trình bày phương sai [] trên một loạt các loại dữ liệu & nbsp; & nbsp;
Code #3 :
Demonstrates the use of xbar parameter
Python3
import
statistics
sample
=
[
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000060
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000062
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____14
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____16
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000068
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____11
Đầu ra: & nbsp; & nbsp;
Variance of Sample set is 0.36566666666666672
Variance of Sample set is 0.36566666666666673
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.1761300000000000681
& nbsp; & nbsp; mã số 2: trình bày phương sai [] trên một loạt các loại dữ liệu & nbsp; & nbsp;
Đầu ra: & nbsp; & nbsp;
Variance of Sample set is 0.3656666666666667
& nbsp; & nbsp; mã số 2: trình bày phương sai [] trên một loạt các loại dữ liệu & nbsp; & nbsp;
Code #4 : Demonstrates the
Error when value of xbar is not same as the mean/average value
Python3
import
statistics
sample
=
[
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000060
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000062
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____14
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____16
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000068
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____11
Đầu ra: & nbsp; & nbsp;
& nbsp; & nbsp; mã số 2: trình bày phương sai [] trên một loạt các loại dữ liệu & nbsp; & nbsp;
Đầu ra: & nbsp; & nbsp;
0.3656666666663053
& nbsp; & nbsp; mã số 2: trình bày phương sai [] trên một loạt các loại dữ liệu & nbsp; & nbsp;
Code #4 : Demonstrates StatisticsError
Python3
import
statistics
sample
=
[
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000060
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000062
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____14
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____16
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000068
Variance of Sample 1 is 15.80952380952381 Variance of Sample 2 is 3.5 Variance of Sample 3 is 61.125 Variance of Sample 4 is 1/45 Variance of Sample 5 is 0.176130000000000061____11
Variance of Sample set is 0.36566666666666672
Variance of Sample set is 0.365666666666666719
Đầu ra: & nbsp; & nbsp;
Traceback [most recent call last]: File "/home/64bf6d80f158b65d2b75c894d03a7779.py", line 10, in print[statistics.variance[sample]] File "/usr/lib/python3.5/statistics.py", line 555, in variance raise StatisticsError['variance requires at least two data points'] statistics.StatisticsError: variance requires at least two data points
& nbsp; & nbsp; mã số 2: trình bày phương sai [] trên một loạt các loại dữ liệu & nbsp; & nbsp;
Applications :
Variance is a very important tool in Statistics and handling huge amounts of data. Like, when the omniscient mean is unknown
[sample mean] then variance is used as biased estimator. Real world observations like the value of increase and decrease of all shares of a company throughout the day cannot be all sets of possible observations. As such, variance is calculated from a finite set of data, although it won’t match when calculated taking the whole population into consideration, but still it will give the user an estimate which is enough to chalk out other calculations.