Make up a set of 7 numbers having the following landmarks:
mode:21
median:24
maximum:35
range:20
I do not understand.
To make the numbers, we need to know each of the properties.
We now know that there are 7 numbers.
Mode is the number with the most occurrence. For example, in the set {18,21,21,22,25,26,29}, 21 is the mode.
Median is the middle number, when the numbers are sorted in sequence. In the above set, 22 is the median.
The maximum in the above is 29, and the range is 29-18=11.
So now can you take it from here?
No, I still do not understand. why did you subtract 29 from 18? what do you do with 11?
The range is the difference between the maximum(29) and the minimum(18), so the range is 11.
For a given range and a maximum, the minimum can therefore be found by subtracting the range from the maximum.
To create a set of 7 numbers with the given landmarks, we need to consider the properties of mode, median, maximum, and range.
1. Mode: The mode is the value(s) that appears most frequently in a set. In this case, the mode is given as 21, meaning that one number in the set should appear more than any other number.
2. Median: The median is the middle value when the set is arranged in ascending order. Since the median is given as 24, we need to place a number in the middle of the set that has 3 numbers before and after it when arranged in ascending order.
3. Maximum: The maximum is the largest value in the set. It is explicitly given as 35, so one number in the set should be 35.
4. Range: The range is the difference between the maximum and minimum values. In this case, the range is given as 20, so the difference between the largest and smallest numbers should be 20.
Based on these landmarks, let's construct a set of 7 numbers:
1. Start by including the number 35 since it has to be the maximum.
Set: {35}
2. Next, add the mode 21. Since mode indicates the number that appears most frequently, we can include it multiple times.
Set: {35, 21, 21}
3. To find the median, we need a number in between the other numbers. Since we have two 21's, place the median number between them. Therefore, the median is 24.
Set: {35, 21, 24, 21}
4. Now let's find the remaining numbers to complete the range. The difference between the maximum (35) and the minimum (x) should be 20. Therefore, x (the smallest number) should be 15.
Set: {35, 21, 24, 21, 15}
5. To ensure the range is 20, we need to find the largest number (y) that is 20 units away from the smallest number (15). Therefore, y is 35.
Set: {35, 21, 24, 21, 15, 35}
6. We still have one number left to complete the set. To avoid altering the mode, median, maximum, and range, we can introduce a unique number. Let's use the number 3.
Set: {35, 21, 24, 21, 15, 35, 3}
So, a possible set of 7 numbers that fits the given landmarks is {35, 21, 24, 21, 15, 35, 3}.