Question

You can only use the numbers; 0, 1, 2, 2.5, 3, 7, 7.5, 9, and 10 to answer the following questions

1. List five numbers with a mean of 5 and a median of 2.5

2. If a list of five numbers has a mean of 5, what is the largest median that this set of data can have?

Answer 1

Answer:

1. no answer

2. medium=3

Step-by-step explanation:

1. Set the five number a,b,2.5,c,d (median=2.5)

mean=5 => a+b+2.5+c+d=5*5=25

because c=2.5, so 7.5 must be  d or e

=>a+b+(d or e)= 25-2.5-7.5=15

(0,1, 2, 3, 7, 9, 10) only 2,3,10 can make it,

but 2, 2.5, 3, 7.5, 10 won't make 2.5 the medium

so, there no answer

2. make it a, b, c, d, e

mean=5 => a+b+c+d+e=5*5=25 (odd)

even (0,2,10) odd (1,3,7,9) and (2.5, 7.5)

odd+odd=even

odd=odd+even+even+even+even (not fit, only 3 even)

or      odd +odd+odd+even+even (1,2,3,9,10)

or       odd+odd+odd+odd+odd (not fit , only 4 odd)

or.    odd+odd+odd+2.5+7.5 (not fit, sum of 3 odd= 15)

or.    odd even+enen+2.5+7.5  (2, 2.5, 3, 7.5, 10)

2, 2.5, 3, 7.5, 10, medium=3

1,2,3,9,10, medium=3

so the largest medium = 3

Answer 2

From the given numbers, we can answer the questions as;

1) There are no 5 numbers from the available ones that can give a mean of 5 and a median of 2.5.

2) The largest median that the set of values with mean of 5 can have is 3.

• We are given the available numbers as;

0, 1, 2, 2.5, 3, 7, 7.5, 9 and 10

• 1. We want 5 numbers that their median is 2.5 and mean is 5.

Let the 5 numbers be a, b, c, d, e.

When, dealing with the median, we have to arrange the numbers in ascending order with the median being at the center.

Thus, we have; a, b, 2.5, d, e

We are told the mean is 5.

If mean is 5 and we have 5 numbers, then;

total of the 5 numbers = 5 × 5 = 25

• Since we know the total is 25 and the median is 2.5, it means the sum of the other 4 numbers = 25 - 2.5 = 22.5

This implies that;

a + b + d + e = 22.5

From the available numbers before 2.5, the maximum combination is 1 + 2 = 3. Thus, if we select a = 1 and b = 2, then;

d + e = 22.5 - 3

d + e = 18.5

There is no combination of two numbers after 2.5 from the ones given that add up to 18.5. Therefore, we will conclude that there are no 5 numbers from the given ones that can fulfil the mean and median condition here.

 

 

• 2) Just like in answer 1 above, let the five digit number be a, b, c, d, e

Since mean is 5, the total is 5 * 5 = 25.

Thus;

a + b + c + d + e = 25

Since the sum is odd, from addition to get an odd number, we know that the odd numbers have to be 1 more than the even numbers to get odd number.

Thus, the possible combinations that can add up to 25 are;

1, 2, 3, 9, 10

2, 2.5, 3, 7.5, 10

Looking at these two possible 5 numbers, the median in both cases are 3 and thus, we can say largest median = 3.

Read more at; https://brainly.com/question/2819396  

1,2,3,9,10, medium=3

so the largest medium = 3