Question

Suppose the mean of four test scores is 70. To answer the why or why not, giving an example or counterexample is an option.

a. Is it possible that none of the test scores is a 70? Why or why not?​​____________________________

​​​​​​​​​​_______________________________

b. Is it possible that all four test scores are the same? Why or why not?​​b. _____________________________

​​​​​​​​​​_______________________________

c. Is it possible that all four scores are below 70? Why or why not?​​c. _____________________________

​​​​​​​​​​_______________________________

d. Is it possible that three of the scores are above 70? Why or why not?​​d. _____________________________

Answer 1

a). Yes

We can have multiple values above or below 70that can still sum up to 280

b).yes, if all numbers are 70.

C).no, all numbers can not be below 70.

The sum will not be equal to 280 again

D). Yeah.it is

This is possible if the numbers can still balance up to 280.

Explanation:

Given the mean to be 70 generally.

And total of the score =70*4

Total score = 280.

A). It's possible that the scores none are 70.

We can have values like 69,68,72,71

The above numbers can still give a meam of 70

And a total of 280.

B). It's possible

The test score can be all same if the scores are all 70.

It will still give total of 280 and mean of 70

C). It's not possible

Imagine the numbers are all 69,69,69,69.

Just number below 70 for the four of them will give us total of 276

And a mean below 70.

D). Yeah it is possible

The possibility occurs when the remaining number out of the four is way below 70.

Example.

20, 80,100,80

The sum of the above= 280

Mean = 70