"Variance" PPT courseware 3

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"Variance" PPT courseware 3

1. Assume n data x1, x2,...xn, the average of the squared differences between each data and their average is called the variance, recorded as ____. The variance formula is ______________.

2. The larger the variance, the more ________ the data fluctuates; the smaller the variance, the more ________ the data fluctuates.

1. (5 points) (2013·Chongqing) A special police unit held a 1,000-meter shooting competition in order to select "sharp shooters". In the end, two soldiers, A and B, entered the final. Under the same conditions, they each shot the target 10 times. After statistical calculation, the total scores of two soldiers A and B are both 99.68. The variance of A is 0.28 and the variance of B is 0.21. Then, among the following statements, the correct one is ()

A． A’s grades are more stable than B’s grades

B． B’s grades are more stable than A’s grades

C. The stability of the results of A and B is the same

D. Unable to determine whose performance is more stable

2. (5 points) Given a set of data: 1, 3, 5, 5, 6, the variance of this set of data is ()

A． 16B. 5C. 4D. 3.2

【Error-prone Inventory】

[Example] The average of sample data 3, 6, a, 4, 2 is 5, then the variance of this sample is ()

A． 8B. 5C． 3D. 2

【Incorrect interpretation】D

[Error Cause Analysis] Instead of calculating a based on "the average of data 3, 6, a, 4, 2 is 5", and then finding the variance, we only found the variance of "3, 6, 4, 2".

【correct】

9. (2013·Xianning) Long jump athlete Li Gang tested the training effect. The results of 6 long jumps are as follows: 7.6, 7.8, 7.7, 7.8, 8.0, 7.9. (Unit: m) The average of these six results is 7.8, and the variance is 1/60. If Li Gang jumps twice more, the scores are 7.7 and 7.9 respectively. Then the variance of Li Gang’s 8 long jump scores ______ (fill in “increasing”, “unchanged” or “getting smaller”).

10. It is known that the variance of a set of data x1, x2,... express).

11. (20 points) Uncle Wang contracted two barren hills, A and B, a few years ago, and planted 100 bayberry trees in each, with a survival rate of 98%. I picked bayberries from 4 trees, and the yield of each tree is shown in the line chart.

(1) Calculate the average number of samples from mountains A and B respectively, and estimate the total output of bayberry from mountains A and B;

(2) Try to explain through calculation, which mountain has a more stable yield of bayberry?

1) x A = 40, x B = 40, the total output is 40 × 100 × 98% × 2 = 7 840 (kg)

(2)S²A＝1/4[(50-40)2＋(36-40)2＋(40-40)2＋(34-40)2]＝38,

S²B＝1/4[(36-40)2＋(40-40)2＋(48-40)2＋(36-40)2]＝24,

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Update Time: 2024-10-05

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