數學問題一堆~~高手請進!!

2012-08-23 6:27 am

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1. If the median of the six numbers 6, 12, 20, 13, 8 and x is 11, find the value of x.

2. If the median of the seven numbers 12, 15, 15, 11, 15, 12 and x is 14, find x and the mode of the seven numbers.

3. If the median of the five numbers 16, x, x-4, x-8 and x+7 is 6, find the mean of the five numbers.

4. It is known that 7, 12, 13, 10, x and y are six different integers. Their mean is 12 and their median is 12.5, find the values of x and y.

5. 400 people are chosen from a country and 260 of them are females. Given that the number of males in the country is 92750, estimate the number of population in the country.

6. Consider the following set of data:4, 6, 9, 2, 6, 7, 3, 8
An integer from 0 to 9 is chosen and added to the set of data. Find the probability that the median of the data remains unchanged.

回答 (1)

PeterChow

2012-08-23 3:37 pm

✔ 最佳答案

1.
Rearrange the numbers without x in ascending order:6, 8, 12, 13, 20
With trials, the new order becomes 6, 8, x, 12, 13, 20
∴(x+12)/2=11
x+12=33
x=10

2.
Rearrange the numbers without x in ascending order:11, 12, 12, 15, 15, 15
∴It can be easily seen that x = 14 since the above set of numbers does not have 14.

3.
Rearrange numbers with the unknown x: x-8, x-4, x, x+7
Since 16 is not a possible answer, 16 is the largest number.
∴The new order becomes x-8, x-4, x, x+7, 16
∴x=6
∴The mean of the numbers = (6-8+6-4+6+6+7+16)/5=7

4.
Rearrange the order without x and y: 7, 10, 12, 13
(7+12+13+10+x+y)/6=12
x+y=30
Also, (12+13)/2=12.5, which satisfies one of the requirements.
∴12 and 13 must be in the middle.
With no unknown is fixed, there are many possible answers:
x=1, y=29
x=2, y=28
x=3, y=27
x=4, y=26
x=5, y=25
...

5.
Let x be the number of females in the country.
260:400-260 = x:92750
x = 172250
∴The total population is 172250+92750=265000

6.
Rearrange the order of the numbers: 2, 3, 4, 6, 6, 7, 8, 9
The median=(6+6)/2=6
When 1 integer is added, one of the 6s will be in the 5th term.
The median of 9 terms of numbers is the 5th term number.
∴All numbers do not affect the median.
∴P(the median remains unchanged)=1

參考: me

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