For 3 collections, the mode was 126 and the range is 26. What are the 2 possibilities for the number of items in each collection?
No it is not the answer
To find the possibilities for the number of items in each collection, we need to consider the range and mode of the collections.
Given:
Mode = 126
Range = 26
The mode is the value that appears most frequently in the collection, while the range is the difference between the highest and lowest values in the collection.
Let's consider the possibilities step-by-step:
1. Start by assuming the mode is the maximum value in one of the collections.
Case 1: Mode is the maximum value in one of the collections
If the mode, 126, is the maximum value in one of the collections, the minimum value can be calculated by subtracting the range from the mode.
Minimum Value = Mode - Range
Minimum Value = 126 - 26
Minimum Value = 100
Case 2: Mode is the minimum value in one of the collections
If the mode, 126, is the minimum value in one of the collections, the maximum value can be calculated by adding the range to the mode.
Maximum Value = Mode + Range
Maximum Value = 126 + 26
Maximum Value = 152
So, the two possibilities for the number of items in each collection are:
1. Minimum Value = 100, Maximum Value = 126
2. Minimum Value = 126, Maximum Value = 152
To find the possibilities for the number of items in each collection, we need to consider the mode and the range of the collections.
Let's denote the number of items in the first collection as x, the second collection as y, and the third collection as z.
Given that the mode is 126, it means that 126 appears most frequently in the collections. So, we need to find the values of x, y, and z that satisfy this condition.
Now, let's consider the range. The range is the difference between the maximum and minimum values in a collection. Given that the range is 26, we can write two different equations based on the values of x, y, and z:
1. The maximum value - the minimum value = 26
This equation can be written as (x + 26) - x = 26, which simplifies to 26 = 26. This equality always holds true, so this equation does not provide any useful information.
2. The three values (x, y, and z) should be larger than the mode (126), and the difference between the largest and smallest value should be 26.
This can be written as (x - 126) + (y - 126) + (z - 126) = 26.
Simplifying this equation gives us x + y + z = 426.
To find the possibilities, we need to search for integer solutions for x, y, and z that satisfy both equations.
One possible solution is:
x = 150, y = 150, z = 126.
In this case, the maximum value in the collection is 150, the minimum value is 126, and the range is 150 - 126 = 26. Additionally, the mode is 126.
Another possible solution is:
x = 126, y = 150, z = 150.
In this case, the maximum value in the collection is 150, the minimum value is 126, and the range is 150 - 126 = 26. Moreover, the mode is 126.
Therefore, the two possibilities for the number of items in each collection are either (150, 150, 126) or (126, 150, 150).
I'm not sure what you are asking.
126 what?
If the mode is 126 and the range is from 120 to 146, you have a positively skewed distribution.
If the mode is 126 and the range is from 104 to 130, you have a negatively skewed distribution.
If the range is 133-159, then it approximates a normal distribution.
Does this answer your question?