The interquartile range is the difference between the third and first quartiles - that is, the 75th percentile and the 25th percentile. Knowing both is necessary and sufficient.

Statement (1) alone does not give us any information to find out the age of Lilly, therefore it is not sufficient.

Statement (2) alone does not give us enough information to determine the ages of each kid. Therefore it is not sufficient.

Statement (1) and (2) give us the following information:

A = 6 and A + L = 13, therefore L = 13 - 6 = 7

With the ages of both kids we can find the new age range = 8 - 2 = 6

Statement (1) indicates that the range of the numbers is 20. The range is the difference between the highest number and the lowest number. The difference between each pair of numbers in the list is less than 20. Therefore, n is the lowest number in the list. We can then calculate n as follows:

Therefore Statement (1) is SUFFICIENT.

Statement (2) states that n<5 which means n is the lowest number in the list. However this information alone is not sufficient to find the value of n.

Therefore Statement (2) is not SUFFICIENT.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.

The range of a set of numbers is the difference between the maximum and the minimum values of these numbers. In order to determine the range of these numbers, we need to know the values of n and 2n-1 or at least we should know that n and 2n-1 are not the minimum or the maximum values, meaning n and 2n-1 do not affect the range of these numbers.

(1) 

Therefore n is not the minimum value in this list. However, we do not if 2n-1 is the maximum value. Statement (1) ALONE is not sufficient.

(2)

n and 2n-1 do not affect the range then. The range of these numbers is:

Statement (2) ALONE is sufficient.

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