In this case, average is also the middle value.

The arithmetic mean of a data set is the sum of the values divided by the number of values in the set. Since we know that there are 20 values, all we need is the sum of the values. The sum can be easily deduced to be 2,000 from either one of the statements, so the arithmetic mean can be determined to be .

The answer is that either statement alone is sufficient.

The number of sample for each town = 6; N=6; E = 6-1 = 5

Overall average (of all 18 establishments) = 177.5 = O

Number of towns (columns) = 3; V1=3-1=2

total samles = 18; V2=18-3 = 15

For an F value of 2.13 with V1=2 and V2 = 15, p = .153

So, we can not reject the null hypothesis because our data would occur 15% of the time assuming the 3 averages are equal.  

Note - the cutoff F value for 95% is 3.68

Knowing the median score is neither necessary nor helpful. What will be needed is the sum of the scores so far and the number of tests Joe has taken. But the number of tests taken is not given, and without this, there is no way to find the sum either.

The mean of a data set requires you to know the sum of the elements and the number of elements; you know the latter, but neither statement alone provides any clues to the former.

However, if you know both, you can add both sides of the equations as follows:

Rewrite as:

and divide by 9:

Now you know the sum, so divide it by 6 to get the mean:

 .

Statement 1 can be used to find the arithmetic mean by combining the information. For statement 1, the average for the last seven days is found by reversing the arithmetic mean equation. Let be the sum of the degrees for the past 3 days. Let  be the sum of the degrees for the 4 days before that. Then we get

 and  so we can solve and find  and .

Also, we know  = the arithmetic mean for the last week.

So  

Statement 2 can be used to find the arithmetic mean using the arithmetic mean formula. This is the total sum, divided by the number of days. Thus, 

Multiply the second equation by 2 on each side, and add it to the first equation.

Divide this sum by 5:

3 numbers are given in increasing order.

I. The second number is given.

is determined

II. The arithmetic mean of the first and third numbers is given.

is given, and therefore is given.

We are given a system of equations by the prompt:

The arithemetic mean of the first two is 5 less than the arithmetic mean of all three.

The sum of the first two numbers is equal to the arithmetic mean of the last two.

Combining these two, we get:

Thus, the second statement doesn't actually provide us with any information (we are still left with 2 equations and 3 variables, which cannot be solved for any particular number).

On the other hand, if y is determined, then relates and .  Similarly,  relates and .  Since these give different equations, we could use them to solve for both and .

So the first gives sufficient data while the second does not.

For statement (1), there are different combinations that satisfy the condition. For example, the five numbers can be  or the five numbers can be . Therefore, we cannot determine how many of the numbers are greater than  by knowing the first statement.

For statement (2), even though we know three of them, the two unknown numbers can both be greater than , or one smaller and one greater. Thus statement (2) is not sufficient.

Putting the two statements together, we know that the sum of the two unknown numbers is

Since none of them is greater than 100, both of them have to be greater than 50. Therefore when we combine the two statements, we know that there are two numbers that are greater than 50.

The median gives information about the center of a set of numbers, but is insufficient for calculating the mean. Additionally, the mode merely indicates which number is the most repeated value. Therefore, more information is required to calculate the mean.