Question

HELP TIME CRUNCH! MARK BRAINLIEST! THX! 30 POINTS

There is a set of five positive integers whose average (mean) is 5, whose median is 5, and whose only mode is 8. What is the difference between the largest and smallest integers in the set?

A sample consisting of five observations has an arithmetic mean of 12 and a median of 14. What is the smallest value that the range (largest observation minus smallest) can assume for such a sample?

The mean of a set of five different positive integers is 15. The median is 18. Find the maximum possible value of the largest of these five integers.

Answer 1

Answer:

Question 1: 7

Question 2: I couldn't figure it out :(

Question 3: 35 I think

Step-by-step explanation:

Question 1

A set of five positive integers: a+b+c+d+e

Whose mean is 5: $\frac{a+b+c+d+e}{5}=5$

Whose median is 5: $\frac{a+b+5+d+e}{5}=5$

Whose only mode is 8: $\frac{a+b+5+8+8}{5}=5$

The reason the last two digits are 8 is because the only mode is 8, and there are only two digits greater than 5, and 8 > 5.

Let's multiply both sides of the equation by 5: a+b+5+8+8=25

Simplify: a+b+21=25

Simplify further: a+b=4

Only possible values are a=1, and b=3.

Now, go back to the original expression, but substitute in a and b

1+3+5+8+8

8-1=7

Question 2

I'm really sorry, but I had some trouble on this one

Question 3

A set of five different positive integers: a+b+c+d+e

Whose mean is 15: $\frac{a+b+c+d+e}{5}=15$

Whose median is 18: $\frac{a+b+18+d+e}{5}=15$

Simplify: a+b+18+d+e=75

Simplify further: a+b+d+e=57

We know that a<b<18<d<e.

We want the maximum possible value for e.

set all other digits as low as possible (remember they are integers, so no fractions or decimals)

1+2+19= 22, 57-22=35

*I am not 100% sure if this last one is correct because it is not on my RSM homework so I can not check.

Answer 2

Answer:

7

Step-by-step explanation:

Question 1

A set of five positive integers: a+b+c+d+e

Whose mean is 5

Whose median is 5

Whose only mode is 8

Start by multiplying both sides of the equation by 5: a+b+5+8+8=25

Simplify by adding: a+b+21=25

Simplify by inverse operation: a+b=4

Now the only possible values are a=1, and b=3.

The original expression, with a and b substituted

1+3+5+8+8

8-1=7