Create a set of data with 5 numbers that satisfy all of the following conditions:
1. the range is 10
2. the mean is 20
3. the median is 22
mean 20
20
range 10
15 20 25
median 22
15 15 22 23 25
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To create a set of data with 5 numbers satisfying the given conditions, we need to consider the properties of range, mean, and median.
Range:
The range is the difference between the maximum and minimum values in a dataset. In this case, the range should be 10. To achieve this, we can select the minimum value as (mean - range/2 = 20 - 10/2 = 15) and the maximum value as (mean + range/2 = 20 + 10/2 = 25).
Mean:
The mean is the average of all the numbers in a dataset. In this case, the mean should be 20. However, since we are creating a set with just 5 numbers, only having the mean at 20 might not ensure that the median is also 22. Therefore, we will aim for a symmetrical distribution to achieve this.
Median:
The median is the middle value in a set of numbers when they are arranged in ascending or descending order. In this case, the median should be 22. To accomplish this, we need to introduce two numbers lower than 22 and two numbers higher than 22.
Here's one possible set of data that satisfies all the given conditions:
{15, 18, 22, 25, 28}
Explanation:
- The minimum value is 15 and the maximum value is 28, giving us a range of 10 (28 - 15 = 13).
- The sum of all the numbers is 15 + 18 + 22 + 25 + 28 = 108. Dividing this by the total number of elements (5) gives us a mean of 21.6, which is close to the target mean of 20.
- Arranging the numbers in ascending order {15, 18, 22, 25, 28}, we can see that the median is indeed 22.
Note that there could be multiple sets of data that satisfy these conditions, but this is just one example.