"Variance" PPT courseware 2

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"Variance" PPT courseware 2

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1. The difference between the maximum data and the minimum data in a set of data is called the range, that is, range = maximum data - minimum data.

2. Range reflects the fluctuation range of a set of data, and using range to describe the degree of dispersion of this set of data is simple and clear. The larger the range, the greater the dispersion of the data.

3. Since the range ignores the differences between all data in a set of data and is only determined by the maximum and minimum values, individual extreme values ​​far away from the group will affect the range to a large extent, so the range is often It cannot fully reflect the actual discrete degree of a set of data.

Since the deviation may be a positive number, zero, or a negative number, when finding the sum of the deviations, the positive and negative numbers just cancel each other out, and the result is zero. Therefore, the sum of the deviations cannot be used to express the degree of dispersion of a set of data.

In order to characterize the degree of dispersion of a set of data, the average of the squared deviations is usually used to describe it.

In a set of data, the average of the squares of the differences between each data and their mean is called the variance of the set of data, usually represented by S2, that is

S2=1/n[(x1－x) 2+(x2－x) 2+(x3－x) 2+····+(xn－x) 2]

The smaller the variance, the smaller the dispersion of this set of data, the more concentrated the data, and the more representative the average.

Class summary

1. In a set of data, the difference between each data and the mean is called the deviation of this data. Deviation can reflect the degree to which a data deviates from the mean.

Since the deviation may be a positive number, zero, or a negative number, when finding the sum of the deviations, the positive and negative numbers just cancel each other out, and the result is zero. Therefore, the sum of the deviations cannot be used to express the degree of dispersion of a set of data.

2. In a set of data, the average of the squares of the differences between each data and their average is called the variance of the set of data, usually represented by S2, that is

S2=1/n[(x1－x) 2+(x2－x) 2+(x3－x) 2+····+(xn－x) 2]

The smaller the variance, the smaller the dispersion of this set of data, the more concentrated the data, and the more representative the average.

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Update Time: 2024-08-16

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