"Variance" PPT courseware

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"Variance" PPT courseware

Coach's troubles

Two shooters, A and B, now want to choose a shooter to participate in the competition.

If you were a coach, which one do you think is more suitable?

The test results of shooters A and B are as follows:

⑴ Please calculate the average scores of the two shooters respectively;

⑵ Please draw a line statistical chart in the figure below based on the results of these two shooters;

⑶ Now we need to select a shooter to participate in the competition. If you are a coach, which one do you think is more suitable? Why?

Who has better stability? What data should be used to measure it?

The sum of the deviations between A’s shooting performance and the average performance:

(7-8)+(8-8)+(8-8)+(8-8)+(9-8)=0

The sum of the deviations between B’s shooting score and the average score:

(10-8)+(6-8)+(10-8)+(6-8)+(8-8)=0

|7-8|+|8-8|+|8-8|+|8-8|+|9- 8|=2

The sum of the absolute values ​​of the deviations between B’s shooting performance and the average performance:

|10-8|+|6-8|+|10-8|+|6-8|+|8- 8|=8

The sum of squares of the deviations between A's shooting performance and the average performance:

(7-8)2+(8-8)2+(8-8)2+(8-8)2+(9-8)2=2

The sum of squares of the deviations between B’s shooting performance and the average performance:

(10-8)2+(6-8)2+(10-8)2+(6-8)2+(8-8)2=16

What else is related to the sum of the squares of the above deviations?

How to measure stability when the number of shots is different?

generalize

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

S2=1/n[(x1-x)2+ (x2-x)2 +…+ (xn-x)2 ]

The steps for calculating the variance can be summarized as "average first, then find the difference, square it, and then average".

Variance is used to measure the fluctuation of a batch of data (that is, the deviation of this batch of data from the mean).

The larger the variance, the greater the fluctuation of the data and the more unstable it is.

Feedback in class:

1. Select one shooter from A and B to participate in the competition.

In the preliminaries, each of them fired 10 bullets, and the number of hits was as follows:

A: 9, 8, 9, 9, 8, 9.5, 10, 10, 8.5, 9;

B: 8.5, 8.5, 9.5, 9.5, 10, 8, 9, 9, 8, 10.

Then the average of A is ______, and the average of B is ______.

Do you think it would be more appropriate to send ______ to participate in the competition?

Please explain with calculations.

Test feedback:

(1) There are 5 numbers 1, 4, a, 5, and 2. The average is a, then the variance of these 5 numbers is _____.

(2) The variance of all integers whose absolute value is less than _______ is ______.

(3) A set of data: a, a, a, ---, a (there are n a), then its variance is ___;

Please use your findings to solve the following problems:

It is known that the mean of data a1, a2, a3,...,an is X and the variance is Y, then

①The average of data a1+3, a2 + 3, a3 +3,..., an +3 is ------, and the variance is ------

②The average of data a1-3, a2 -3, a3 -3,..., an -3 is --------, and the variance is ------

③The average of data 3a1, 3a2, 3a3,...,3an is --------, and the variance is -------.

④The average of data 2a1-3, 2a2 -3, 2a3 -3,..., 2an -3 is --------, and the variance is -------.

If the same non-zero constant is added to each data in a set of data, then (　) of this set of data

A． Both the mean and variance remain unchanged

B． The mean does not change, the variance changes

C. The mean changes, the variance remains the same

D. Both the mean and variance change

Two students, A and B, each did 5 standing long jump tests before taking this year's physical education exam. Their average scores were the same. The variance of A's scores was 0.005. B's scores were as follows: 2.20m, 2.30m, 2.30m, 2.40m, 2.30m, then the results of A and B are compared (　)

A． A's results are more stable

B． B’s results are more stable

C. The results of A and B are equally stable

D. Not sure whose performance is more stable

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Update Time: 2024-11-14

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