Photo AI
Write three integers into the following boxes so that the three numbers have: - a mode of 2 - a mean of 5 Answer: _____, _____, and _____ Write five integers into the following boxes so that the five numbers have: - a mode of 4 - a median of 4 - a mean of 5 - a range of 12 Answer: _____, _____, _____, _____, and _____ - Junior Cycle Mathematics - Question 10 - 2021
Question 10
Write three integers into the following boxes so that the three numbers have: - a mode of 2 - a mean of 5 Answer: _____, _____, and _____ Write five integers into ... show full transcript
Worked Solution & Example Answer:Write three integers into the following boxes so that the three numbers have: - a mode of 2 - a mean of 5 Answer: _____, _____, and _____ Write five integers into the following boxes so that the five numbers have: - a mode of 4 - a median of 4 - a mean of 5 - a range of 12 Answer: _____, _____, _____, _____, and _____ - Junior Cycle Mathematics - Question 10 - 2021
Step 1
Write three integers into the following boxes so that the three numbers have: a mode of 2 and a mean of 5
Answer
To achieve a mode of 2, the integer 2 must appear more frequently than any other number. Since we need three integers and the mean must be 5, we can set two of the integers to 2 and the third integer to a value that satisfies the mean condition.
-
Set two integers to 2:
- First Integer: 2
- Second Integer: 2
-
Calculate the third integer using the mean formula:
-
Mean formula:
-
Given:
-
Let the third integer be x:
-
This simplifies to:
-
Thus, the third integer should be 6:
-
Third Integer: 6
-
Thus, the integers are 2, 2, and 6.
Step 2
Write five integers into the following boxes so that the five numbers have: a mode of 4, a median of 4, a mean of 5, and a range of 12
Answer
To achieve the required conditions, we need to choose five integers with careful consideration to meet all criteria:
-
For the mode to be 4, the number 4 must occur most frequently. Let's choose it twice:
- First Integer: 4
- Second Integer: 4
-
For the median to be 4, the numbers must be ordered such that the middle number is 4. Let's initially place the known numbers for clarity:
- First Integer: 4
- Second Integer: 4
-
Fill in the remaining three integers. Since the median is 4, we can add one more 4 to in the middle of the order:
- Third Integer: 4
-
Now we will add two additional integers that fit our conditions:
-
To meet the mean of 5:
-
Let’s say we choose the fourth Integer: 6 and the fifth Integer: 12.
-
The integers we now have are 4, 4, 4, 6, and 12.
-
-
Calculating the range:
-
The range is max value - min value:
-
Thus, the range is 12 - 4 = 12.
-
So, the complete set of integers is 4, 4, 4, 6, and 16.