"The Dispersion Degree of Data" Data Analysis PPT Courseware 3

Description

"The Dispersion Degree of Data" Data Analysis PPT Courseware 3

learning target

1. Understand the concepts of the three measures that describe the degree of dispersion of data - range, variance and standard deviation.

2. Be able to use a calculator to find the numerical values ​​of range, variance and standard deviation, and apply them in specific problems.

3. Experience the exploration of several quantities that represent the degree of data dispersion, and experience the idea of ​​using samples to estimate the population.

The quality inspector sampled 20 chicken legs from the products of factories A and B respectively. The mass (unit: g) is as follows:

Factory A: 75 74 74 76 73 76 75 77 77 74

74 75 75 76 73 76 73 78 77 72

Factory B: 75 78 72 77 74 75 73 79 72 75

80 71 76 77 73 78 71 76 73 75

Question 1: If we only consider the specifications of chicken legs, which factory do you think a foreign trade company should buy chicken legs from?

Question 2: Can you estimate from the picture the average quality of chicken legs randomly inspected in factories A and B?

Question 3: Observe the two charts to see the distribution of the mass of the randomly inspected chicken legs. What do you find?

in conclusion

The average quality can only reflect the overall centralization trend, but cannot reflect individual changes. From the picture, the products of Factory A are more in line with the requirements.

The specifications of chicken legs from Factory A are relatively stable, with only a 6g difference between the maximum and minimum values;

The specifications of chicken legs from Factory B are relatively unstable, with a difference of 9g between the maximum and minimum values.

From this question we found:

1. For data analysis, the average can only reflect their average value, and it still has great limitations in the research of practical problems.

For example, in the above question, the average number is 75. In fact, the products of Factory A are more in line with the requirements.

2. Discuss that the degree of dispersion of data can be characterized by the statistic "range".

The larger the range, the greater the deviation from the average, and the more unstable the quality (performance) of the product.

Class summary

Through the study of this lesson, we need to master:

1. The degree of dispersion of a set of data can be characterized by three statistics: range, variance, and standard deviation. The smaller the range, variance, or standard deviation of a set of data, the more stable the set of data is.

2. Variance (standard deviation) can better describe the fluctuation of data as a whole than range, and is one of the most commonly used statistics in statistics.

3. The variance (standard deviation) is calculated according to the formula.

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Update Time: 2024-10-01

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