For statement (1), since we don’t know the value of each number, we cannot calculate the average of the sequence. For statement (2), the mode of the sequence is 3 means that “3” occurs most times in the sequence, but we cannot get to the average because we don’t know the value of other numbers. If we look at the two conditions together, we will know that there are 2 or 3 “3”'s in the sequence, but we don’t know exactly how many times “3” occurs. If the 3 numbers are all “3”s, then we can answer the question; If not, then we cannot answer the question. Thus both statements together are not sufficient.

We are looking for an average here. Statement 1 tells us we are looking for even consecutive integers such as 2, 4, 6, 8, and 10. Statement 2 tells us the difference between the smallest and largest integer; however, the difference between the largest and smallest of five consecutive even (or odd) integers will ALWAYS be 8, regardless of what 5 consecutive integers we choose; therefore the two statements don't give us enough information to solve for the average. 

Statement 2 does not provide enough information about the mean as it can vary greatly from the median. Statement 1 is sufficient to calculate the mean, because even though it is impossible to calculate the set of numbers, the mean is calculated by dividing the sum by the total number of incidences in the set.

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: