"Data Fluctuations" Data Collection and Processing PPT Courseware 3

Description

"Data Fluctuations" Data Collection and Processing PPT Courseware 3

problem situation

In order to improve the international competitiveness of agricultural and sideline products, some industry associations have divided the planning of agricultural and sideline products. A foreign trade company wants to export a batch of 75g chicken legs. There are currently two manufacturers providing supply. Their prices are the same and the quality of the chicken legs is similar.

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

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

74 75 75 76 73 76 73 78 77 72

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

80 71 76 77 73 78 71 76 73 75

(1) Can you estimate the average mass of chicken legs sampled from factories A and B from the picture?

(2) Find the average mass of chicken legs sampled from factories A and B, and draw a straight line representing the average mass on the graph.

(3) What is the maximum mass of the 20 chicken legs sampled from Factory A? What is the minimum value? How many grams are they different? Second?

(4) If you only consider the specifications of chicken legs, which factory do you think a foreign trade company should purchase chicken legs from?

think about it

Among the above questions, which quantity do you think is a quantity that reflects the degree of discreteness of the data?

Range is a statistic that describes the degree of dispersion of data.

The difference between the maximum value and the minimum value in a set of data is the range

From the above discussion, we can see that sometimes range cannot measure the fluctuation of data.

Mathematically, the degree of dispersion of data can also be characterized by variance or standard deviation.

Definition

Variance: the average of the squared differences between each data and the mean

S²=1/n[(x1-x)²+(x2-x)²+......(xn-x)²]

The arithmetic square root of the variance is the standard deviation

Do it

1. Calculate the variance of the quality of 20 chicken legs sampled from factories A and C respectively.

2. Based on the calculation results, which company’s product do you think is more in line with the specifications?

practice

1. Book P174 Practice in class

A: The average is 178cm, the range is 2cm, and the variance is 0.6

B: The average is 178cm, the range is 4cm, and the variance is 1.8

2. For data 3, 2, 1, 0, -1,

Its range is _________.

Its variance is _________.

Its standard deviation is _________.

Class summary

1. There is more than one quantity that describes the fluctuation size of a set of data. The most commonly used quantities are range, variance, and standard deviation.

2. Generally speaking, the smaller the range, variance, or standard deviation of a set of data, the more stable the set of data is.

3. When actually writing, the range and standard deviation have units, and the variance does not need to be marked with units.

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"Data Fluctuations" Data Collection and Processing PPT Courseware 2:

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Update Time: 2024-09-08

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