Maths Olympiad Prep

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Algebra Difficulty 3.0 AMC 10/12 Find the answer

Given that s2\= 14\frac {1}{4}(3.2- $$\bar{x}$$)2+(5.7- $$\bar{x}$$)2+(4.3- $$\bar{x}$$)2+(6.8-$$\bar{x}$$)2 is the calculation process written by Li Hua when calculating the variance of a set of data, then the value of xˉ\bar{x} is \_\_\_\_\_\_.

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since s2\= 14\frac {1}{4}(3.2- $$\bar{x}$$)2+(5.7- $$\bar{x}$$)2+(4.3- $$\bar{x}$$)2+(6.8-$$\bar{x}$$)2,

We know that xˉ\bar{x} is the mean of 3.2, 5.7, 4.3, and 6.8.

Therefore, xˉ\bar{x} = (3.2 + 5.7 + 4.3 + 6.8) ÷ 4

= 20 ÷ 4

= 5

So the answer is: \boxed{5}.

The variance of a set of data is the average of the squared differences from the mean, so xˉ\bar{x} is the mean of 3.2, 5.7, 4.3, and 6.8. By calculating the mean, we find the value of xˉ\bar{x}.

This problem primarily tests the understanding and calculation of variance. It is essential to master the concept that the variance is the average of the squared differences from the mean.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.