Gladys 写下了四个数。这些数的平均数是 13，中位数是 12，众数是 10。求这四个数。

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完整解法

1. Use the mean to find the total of the four numbers.

Mean $=13$ for $4$ numbers.

$\text{Total}=13\times 4=52$

2. Use the median and mode to determine the four numbers.

Arrange the numbers in ascending order as

$a,\ b,\ c,\ d$

For four numbers, the median is the mean of the two middle numbers.

$\frac{b+c}{2}=12$

$b+c=24$

The mode is $10$ , so $10$ must be repeated. Since the numbers are in ascending order, the first two numbers are

$10,\ 10$

Then

$\frac{10+c}{2}=12$

$10+c=24$

$c=14$

Using the total:

$10+10+14+d=52$

$d=18$

答案

The four numbers are $10,\ 10,\ 14,\ 18$ .

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